Mathematics : asked on shoreelinee1337

31.03.2022

The perimeter of an equilateral triangle is 60 m.the area is

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09.07.2023, solved by verified expert

Mathematics, DAV Post Graduate College

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173.21m^2

Step-by-step explanation:

So lets figure out how to find the formula for the area of a equilateral triangle.

We can immediatly notice that a equilaterial triangle is really just two right triangles merged together at their heights.

This means that the total area of the equilaterial triangle is equivelent to finding the area of 2 right triangles. this would make the formula:

This is a fairly simple formula, and works out nicely since our normal right triangle formula for area of must be multiplied by 2 since there are two right triangles.

The problem is, how we will actually find h, the height.

Each side length of a equilateral triangle equals 1/3 of the perimeter, meaning that each side length is 20.

W, the width of each right triangle is 1/2 of the side length of the equilateral triangle, meaning that the width equals 10.

We also know that the hypotenuse of the triangle is equal to the side length of the equilateral triangle, which means that the hypotenuse equals 20.

We can use this to figure out our unknown height, which we can then use to find our area.

We can figure out this height using teh pythagreon theorm, since

, which we can rewrite to get:

Now we can plug in our hypotenuse and width to solve:

=

=

=

Height = 17.321

Now we can solve for the area using the formula from above,

=

So our area equals 173.21!

Hope this helps! :3

The perimeter of an equilateral triangle is 60, №18009997, 31.03.2022 15:32

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Mathematics

The perimeter of an equilateral triangle is 60 m.the area is

Step-by-step answer

P Answered by Specialist

173.21m^2

Step-by-step explanation:

So lets figure out how to find the formula for the area of a equilateral triangle.

We can immediatly notice that a equilaterial triangle is really just two right triangles merged together at their heights.

This means that the total area of the equilaterial triangle is equivelent to finding the area of 2 right triangles. this would make the formula:

width*height = area

This is a fairly simple formula, and works out nicely since our normal right triangle formula for area of $\frac{length*width}{2}$ must be multiplied by 2 since there are two right triangles.

The problem is, how we will actually find h, the height.

Each side length of a equilateral triangle equals 1/3 of the perimeter, meaning that each side length is 20.

W, the width of each right triangle is 1/2 of the side length of the equilateral triangle, meaning that the width equals 10.

width = 10

We also know that the hypotenuse of the triangle is equal to the side length of the equilateral triangle, which means that the hypotenuse equals 20.

hypotenuse = 20

We can use this to figure out our unknown height, which we can then use to find our area.

We can figure out this height using teh pythagreon theorm, since

$Hypotenuse=\sqrt{width^2+height^2}$ , which we can rewrite to get:

$Height = \sqrt{hypotenuse^2-width^2}$

Now we can plug in our hypotenuse and width to solve:

$Height = \sqrt{20^2-10^2}$

=

$Height = \sqrt{400-100}$

=

$Height = \sqrt{300}$

=

Height = 17.321

Now we can solve for the area using the formula from above, width*height = area

=

10*17.321 = 173.21

So our area equals 173.21!

Hope this helps! :3

The perimeter of an equilateral triangle is 60 m.the area is

Mathematics

How do i find the area of an equilateral triangle given the perimeter of 60 and the height of 17.3 cm?

Step-by-step answer

P Answered by Specialist

1

If perimeter is 60 so the side is 60 ÷ 3 = 20

Now we can apply the area formula for triangles;

$A=\frac{1}{2}.b.h\\
\\
A=\frac{1}{2}.20.17.3=10.17.3=173 \ cm^2$

Mathematics

An equilateral triangle has a perimeter of 60 meters and s height of 17.3 meters. What is the area of the triangle

Step-by-step answer

P Answered by Master

1

The area of the triangle is 173 squared meters.

Step-by-step explanation:

An equilateral triangle has all sides equal to each other.

Finding the length of each side of the triangle.

Like I said before, in an equilateral triangle all the sides are equal. The perimeter of a triangle is every side added together. Since each side is equal, you will divide 60 (the perimeter) by 3 (the number of sides).

$\frac{60}{3} = 20$

Each side is equal to 20 meters.

Finding the area of the triangle

To find the area of a triangle you need the formula: $A = \frac{1}{2} bh$

A is the area, b is the base, and h is the height.

b = 20

h = 17.3

$A=\frac{1}{2} (20)(17.3)$ Multiply what is in the parenthesis first

$A = \frac{1}{2} (346)$ Multiply 346 by 1

$A = \frac{346}{2}$ Divide 346 by 2

A = 173

Mathematics

An equilateral triangle has a perimeter of 60 meters and s height of 17.3 meters. What is the area of the triangle

Step-by-step answer

P Answered by Specialist

1

The area of the triangle is 173 squared meters.

Step-by-step explanation:

An equilateral triangle has all sides equal to each other.

Finding the length of each side of the triangle.

Like I said before, in an equilateral triangle all the sides are equal. The perimeter of a triangle is every side added together. Since each side is equal, you will divide 60 (the perimeter) by 3 (the number of sides).

$\frac{60}{3} = 20$

Each side is equal to 20 meters.

Finding the area of the triangle

To find the area of a triangle you need the formula: $A = \frac{1}{2} bh$

A is the area, b is the base, and h is the height.

b = 20

h = 17.3

$A=\frac{1}{2} (20)(17.3)$ Multiply what is in the parenthesis first

$A = \frac{1}{2} (346)$ Multiply 346 by 1

$A = \frac{346}{2}$ Divide 346 by 2

A = 173

Mathematics

How do i find the area of an equilateral triangle given the perimeter of 60 and the height of 17.3 cm?

Step-by-step answer

P Answered by Specialist

1

If perimeter is 60 so the side is 60 ÷ 3 = 20

Now we can apply the area formula for triangles;

$A=\frac{1}{2}.b.h\\
\\
A=\frac{1}{2}.20.17.3=10.17.3=173 \ cm^2$

Mathematics

An equilateral triangle has a perimeter of 60m and a height of 17.3m. what is its area?

Step-by-step answer

P Answered by PhD

5

The area of any triangle is (1/2) x (length of the base) x (height) .

In this problem, we know the triangle's height,
but what is the length of the base ?

The base is the side that the triangle is sitting on. This particular triangle
is an equilateral one, and its perimeter is 60m. So each side must be 20m.
No matter which side the triangle is sitting on, the length of the base is 20m.

Area = (1/2) x (base) x (height)

Area = (1/2) x (20m) x (17.3m) = 173 m²

Mathematics

An equilateral triangle has a perimeter of 60m and a height of 17.3m. what is its area?

Step-by-step answer

P Answered by PhD

5

The area of any triangle is (1/2) x (length of the base) x (height) .

In this problem, we know the triangle's height,
but what is the length of the base ?

The base is the side that the triangle is sitting on. This particular triangle
is an equilateral one, and its perimeter is 60m. So each side must be 20m.
No matter which side the triangle is sitting on, the length of the base is 20m.

Area = (1/2) x (base) x (height)

Area = (1/2) x (20m) x (17.3m) = 173 m²

Mathematics

CLASS- 9 HERON S FORMULA 1) find the area of an equilateral trimgle whose perimeter is 60cm

Step-by-step answer

P Answered by PhD

1

see below

Step-by-step explanation:

if its perimeter is 60 each side is 60/3 = 20.

Its height will be 10√3 so area is 20 * 10√3 / 2 = 100√3

Mathematics

CLASS- 9 HERON S FORMULA 1) find the area of an equilateral trimgle whose perimeter is 60cm

Step-by-step answer

P Answered by PhD

1

see below

Step-by-step explanation:

if its perimeter is 60 each side is 60/3 = 20.

Its height will be 10√3 so area is 20 * 10√3 / 2 = 100√3

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

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