Find the area of a triangle with base 17 inches and height 22 inches

Choice B) 17.5 feet

A = Area of rectangle

L = length

W = width

The formula to use is A = L*W, so we multiply length and width.

We know W = 7 but we don't know what L is.

We know that A = 122.5 is also given

So let's solve for L

A = L*W

L*W = A

L*7 = 122.5     plug in the given values

7*L = 122.5

7*L/7 = 122.5/7     divide both sides by 7

L = 17.5

He should cut 17.5 feet of streamer. Keep in mind that this only applies if Adrian wants to make the streamer completely taut and a straight line across the ceiling/wall. If he wants the streamer to hang down a bit (forming a shape like a rope bridge in a sense), then the streamer's length will have to be a bit longer to account for the extra distance along the curve.

1. circle T with radius 8 1/2 inches ⇒ answer A

2.  The area of the crust of a 15-inch pizza is 177 inches²  ⇒ answer B

3. 10π feet and 31.4 feet  ⇒ answers B and E

4. The better buy is 10-inch diameter pizza for $8.99 ⇒ answer A

5. The price per square inch is $0.20

6. The largest area of the pond is 1472.61 feet² ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

1.

- A circle is the set of all points in a plane that are a given distance  

 from a fixed point.  

- The given distance is the radius of the circle and the fixed point

 is its center

- A sphere is the set of all points in a space that are a given distance

 from a fixed point.

- The given distance is the radius of the sphere and the fixed point

 is its center

- A circle is 2-Dimensional, but a sphere is 3-Dimensional.

∵ The collection of all points in the same plane that means it is in a  

  2-D dimensional

∴ It is a circle

∵ The collection of all points in the same plane that are 8 1/2  

   inches from Point T

∴ The radius of the circle = 8 1/2 inches and its center is T

* circle T with radius 8 1/2 inches

2.

- The advertised size of a pizza is the diameter of the pizza

∵ The advertised size of a pizza is 15-inch pizza

∴ The diameter of the pizza is 15 inches

∵ The diameter = 2 × radius

∴ The radius = 15 ÷ 2= 7.5 inches

- The area of the circle = πr²

∴ The area of the crust = π(7.5)² = 176.7 ≅ 177 inches²

* The area of the crust of a 15-inch pizza is 177 inches²

3.

- The area of the circle is πr²

- The circumference of the circle is 2πr

- To find the circumference of the circle you must to find the radius

  of the circle from its area

∵ The area of the circle is 78.5 feet²

∵ The area of the circle = πr²

∴ πr² = 78.5 ⇒ divide both sides by π

∴ r² = 78.5/π ⇒ take √ for both sides

∴ r = √(78.5/π)

∵ The circumference of the circle = 2πr

∴ The circumference of the circle = 2π × √(78.5/π) = 31.407

* The circumference of the circle ≅ 31.4 feet

∵ 10π ≅ 31.4  

∴ The answer is 10π feet and 31.4 feet

4.

- To find which pizza is better buy, you must find the price per

  square inch the lowest price will be better

∵ The area of the circle is πr²

∵ r = 1/2 diameter

∵ The price of the 10-inch diameter pizza is $8.99

∵ The radius of it = 1/2 × 10 = 5 inches

∴ Its area = π(5)² = 25π inches²

∵ Its price is $8.99

∴ The price per square inch = 8.99 ÷ 25π ≅ $0.11

∵ The price of the 6-inch diameter pizza is $5

∵ The radius of it = 1/2 × 6 = 3 inches

∴ Its area = π(3)² = 9π inches²

∵ Its price is $5

∴ The price per square inch = 5 ÷ 9π ≅ $0.18

∴ The price of a 10-inch diameter < the price of 6-inch diameter

∴ The better buy is 10-inch diameter pizza for $8.99

5.

∵ The area of the circle is πr²

∵ r = 1/2 diameter

∵ The cost of the circular marble tabletop is $280

∵ Its diameter is 42 inches

∵ The radius of it = 1/2 × 42 = 21 inches

∴ Its area = π(21)² = 441π inches²

∵ Its cost is $280

∴ The price per square inch = 280 ÷ 441π ≅ $0.20

* The price per square inch is $0.20

6.

∵ The pond shaped a circle

- The length of the fence is the circumference of the pond

∵ The circumference of the circle = 2πr

∵ The length of the fence is 136 feet

∴ 2πr = 136 ⇒ divide the two sides by 2π

∴ r = 136/(2π) = 68/π

∵ The area of the circle = πr²

∵ π ≅ 3.14

∴ The area of the pond = 3.14(68/3.14)² = 1472.61

∴ The largest area of the pond is 1472.61 feet²

1. circle T with radius 8 1/2 inches ⇒ answer A

2.  The area of the crust of a 15-inch pizza is 177 inches²  ⇒ answer B

3. 10π feet and 31.4 feet  ⇒ answers B and E

4. The better buy is 10-inch diameter pizza for $8.99 ⇒ answer A

5. The price per square inch is $0.20

6. The largest area of the pond is 1472.61 feet² ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

1.

- A circle is the set of all points in a plane that are a given distance  

 from a fixed point.  

- The given distance is the radius of the circle and the fixed point

 is its center

- A sphere is the set of all points in a space that are a given distance

 from a fixed point.

- The given distance is the radius of the sphere and the fixed point

 is its center

- A circle is 2-Dimensional, but a sphere is 3-Dimensional.

∵ The collection of all points in the same plane that means it is in a  

  2-D dimensional

∴ It is a circle

∵ The collection of all points in the same plane that are 8 1/2  

   inches from Point T

∴ The radius of the circle = 8 1/2 inches and its center is T

* circle T with radius 8 1/2 inches

2.

- The advertised size of a pizza is the diameter of the pizza

∵ The advertised size of a pizza is 15-inch pizza

∴ The diameter of the pizza is 15 inches

∵ The diameter = 2 × radius

∴ The radius = 15 ÷ 2= 7.5 inches

- The area of the circle = πr²

∴ The area of the crust = π(7.5)² = 176.7 ≅ 177 inches²

* The area of the crust of a 15-inch pizza is 177 inches²

3.

- The area of the circle is πr²

- The circumference of the circle is 2πr

- To find the circumference of the circle you must to find the radius

  of the circle from its area

∵ The area of the circle is 78.5 feet²

∵ The area of the circle = πr²

∴ πr² = 78.5 ⇒ divide both sides by π

∴ r² = 78.5/π ⇒ take √ for both sides

∴ r = √(78.5/π)

∵ The circumference of the circle = 2πr

∴ The circumference of the circle = 2π × √(78.5/π) = 31.407

* The circumference of the circle ≅ 31.4 feet

∵ 10π ≅ 31.4  

∴ The answer is 10π feet and 31.4 feet

4.

- To find which pizza is better buy, you must find the price per

  square inch the lowest price will be better

∵ The area of the circle is πr²

∵ r = 1/2 diameter

∵ The price of the 10-inch diameter pizza is $8.99

∵ The radius of it = 1/2 × 10 = 5 inches

∴ Its area = π(5)² = 25π inches²

∵ Its price is $8.99

∴ The price per square inch = 8.99 ÷ 25π ≅ $0.11

∵ The price of the 6-inch diameter pizza is $5

∵ The radius of it = 1/2 × 6 = 3 inches

∴ Its area = π(3)² = 9π inches²

∵ Its price is $5

∴ The price per square inch = 5 ÷ 9π ≅ $0.18

∴ The price of a 10-inch diameter < the price of 6-inch diameter

∴ The better buy is 10-inch diameter pizza for $8.99

5.

∵ The area of the circle is πr²

∵ r = 1/2 diameter

∵ The cost of the circular marble tabletop is $280

∵ Its diameter is 42 inches

∵ The radius of it = 1/2 × 42 = 21 inches

∴ Its area = π(21)² = 441π inches²

∵ Its cost is $280

∴ The price per square inch = 280 ÷ 441π ≅ $0.20

* The price per square inch is $0.20

6.

∵ The pond shaped a circle

- The length of the fence is the circumference of the pond

∵ The circumference of the circle = 2πr

∵ The length of the fence is 136 feet

∴ 2πr = 136 ⇒ divide the two sides by 2π

∴ r = 136/(2π) = 68/π

∵ The area of the circle = πr²

∵ π ≅ 3.14

∴ The area of the pond = 3.14(68/3.14)² = 1472.61

∴ The largest area of the pond is 1472.61 feet²

  C = 22π; A = 121π

Step-by-step explanation:

The relevant formulas for circumference (C) and area (A) are ...

  C = πd . . . . . d is the diameter

  A = πr² . . . . where r = d/2

Filling in the given value for diameter, we have ...

  C = 22π

  A = π(22/2)² = 121π

  C = 22π; A = 121π

Step-by-step explanation:

The relevant formulas for circumference (C) and area (A) are ...

  C = πd . . . . . d is the diameter

  A = πr² . . . . where r = d/2

Filling in the given value for diameter, we have ...

  C = 22π

  A = π(22/2)² = 121π

A 11x16

Step-by-step explanation:

Let the length of rectangle be l and width be w.

Then given that perimeter = 2l+2w = 54

l+w =27

w=27-l

Also area = lw = 176

Substitute for w to get

l(27-l) = 176

-l^2+27l-176=0

(l-16)(l-11)=0

Length = 16 cm

or 11 cm

If length =16 width =11 or if length = 11, width =17

Hence answer is

11x16 i.e. option A

Given is rectangle with perimeter = 54 centimeters and area = 176 squared centimeters.

Let's consider the length of rectangle = L and width of rectangle = W.

We know the following formulas for rectangle :-

Perimeter = 2 x (L + W)

Area = L x W

So we have 2 x (L + W) = 54 and L x W = 176.

L + W = 27 and L x W = 176

We need to find two positive integers such that their sum is 27 and product is 176.

Using trial and error, we have two such positive integers such that 11 + 16 = 27 and 11 x 16 = 176.

So, the dimensions of rectangle would be 11cm x 16cm.

Hence, option A is correct i.e. 11 cm by 16 cm.

A 11x16

Step-by-step explanation:

Let the length of rectangle be l and width be w.

Then given that perimeter = 2l+2w = 54

l+w =27

w=27-l

Also area = lw = 176

Substitute for w to get

l(27-l) = 176

-l^2+27l-176=0

(l-16)(l-11)=0

Length = 16 cm

or 11 cm

If length =16 width =11 or if length = 11, width =17

Hence answer is

11x16 i.e. option A

Given is rectangle with perimeter = 54 centimeters and area = 176 squared centimeters.

Let's consider the length of rectangle = L and width of rectangle = W.

We know the following formulas for rectangle :-

Perimeter = 2 x (L + W)

Area = L x W

So we have 2 x (L + W) = 54 and L x W = 176.

L + W = 27 and L x W = 176

We need to find two positive integers such that their sum is 27 and product is 176.

Using trial and error, we have two such positive integers such that 11 + 16 = 27 and 11 x 16 = 176.

So, the dimensions of rectangle would be 11cm x 16cm.

Hence, option A is correct i.e. 11 cm by 16 cm.