Mathematics: The area of a rectangle is 116 square meter the length is 4 what is the width

The area of a rectangle is 116 square meter the, №10806166, 01.08.2021 09:52

Mathematics

The perimeter of a rectangle is equal to 28 cm. two squares are constructed such that two adjacent sides of the rectangle are each also the side of one of the squares. the combined area of the two squares is 116 cm². find the lengths of the sides of the squares.

Step-by-step answer

P Answered by Master

23

Denote by x the length of the side of the first square and by y the length
of the side of the second square.
We deduce from the figure the following equations:
$x^2+y^2=116\text{ (The combined area)}\\2(x+y)=28\text{ (The perimeter)}\\\text{Solving the above system:}\\x=14-y\text{ then }(14-y)^2+y^2=116\\\text{Solving the above equation for y we get:}\\\text{ Either }y=4\text{ or }y=10.\\\text{The above values corresponds to}\\\text{ Either }x=14-4=10\text{ or }y=14-10=4.$

the length of the sides are 4 and 10.

Mathematics

The perimeter of a rectangle is equal to 28 cm. two squares are constructed such that two adjacent sides of the rectangle are each also the side of one of the squares. the combined area of the two squares is 116 cm². find the lengths of the sides of the squares.

Step-by-step answer

P Answered by Specialist

23

Denote by x the length of the side of the first square and by y the length
of the side of the second square.
We deduce from the figure the following equations:
$x^2+y^2=116\text{ (The combined area)}\\2(x+y)=28\text{ (The perimeter)}\\\text{Solving the above system:}\\x=14-y\text{ then }(14-y)^2+y^2=116\\\text{Solving the above equation for y we get:}\\\text{ Either }y=4\text{ or }y=10.\\\text{The above values corresponds to}\\\text{ Either }x=14-4=10\text{ or }y=14-10=4.$

the length of the sides are 4 and 10.

Mathematics

(08.05, 8.06 MC) Part A: The area of a square is (25x2 - 40x + 16) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (81x2 - 116) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points) (10 points)

Step-by-step answer

P Answered by PhD

Part A: 25x^2-40x+16=(5x-4)^2 because it is in the form of a^2-2ab+b^2 so you know it's a square for sure. So just find the square root of the first and last term to make the equation.

Part B: (81x^2-116)=(9x- $\sqrt{116}$ )(9x- $\sqrt{116}$ )

Mathematics

A rectangle has a total area of 1116 square feet. If the length of the rectangle is 12 ft, what is the width of the rectangle? Please show work!

Step-by-step answer

P Answered by Master

the width of the rectangle is 93

Mathematics

A rectangle has a total area of 1116 square feet. If the length of the rectangle is 12 ft, what is the width of the rectangle? Please show work!

Step-by-step answer

P Answered by Master

the width of the rectangle is 93

Mathematics

A bedroom wall is to be painted around a window as shown below. A rectangle with length 11 feet and width 10 feet. A smaller rectangle with length 3 feet and width 2 feet is cut out of the larger rectangle. What is the area of the wall that will be painted? 6 feet squared 104 feet squared 110 feet squared 116 feet squared

Step-by-step answer

P Answered by Specialist

25

104 ft Squared

Step-by-step explanation:

You are taking away the room area. So 11x10=110 (Area of the whole wall) and you are cutting off 3x2=6 (Area of the wall you are cutting off). So you subtract 110-6= 104 ft2.

Mathematics

An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?

Step-by-step answer

P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45

Mathematics

Use the X method to find the solutions of6x2 + 2x – 20 = 0.

Step-by-step answer

P Answered by PhD