Question

The perimeter of the triangle ABC is equal to the perimeter of a rectangle of length 10 cm and breadth 5 cm. Find the area of the triangle ABC?

Answer 1

Answer:

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Answer 2

The perimeter of the equilateral triangle ABC is equal to the perimeter of a rectangle of length 10 cm and breadth 5 cm. Find the area of the triangle ABC? [Correct Question]

Given:

The perimeter of the equilateral triangle ABC is equal to the perimeter of a rectangle of length 10 cm and breadth 5 cm.

To find:

The area of the triangle ABC

Solution:

We have given the length and breadth of the rectangle as 10 cm and 5 cm respectively then the perimeter of the rectangle is given by:

Perimeter = 2[L+B]

P = 2[10+5]

P = 30 cm

We have;

The perimeter of the equilateral triangle ABC is equal to the perimeter of a rectangle

Let the side of the triangle is a

Then the perimeter of the triangle is 3a

3a = 30

a = 10

And area of the equilateral triangle is given by:

A = $\frac{\sqrt{3} }{4} a^{2}$

A = $\frac{\sqrt{3} }{4} 10^{2}$

A = $\frac{100\sqrt{3}}{4}$

A = 25√3 cm²

Hence,

The area of the triangle ABC is 25√3 cm²