Question

. If area of the square is 100cm2 and its perimeter is same as the perimeter of an

equilateral triangle, what is length of the each side of the triangle?​

Answer 1

Answer:

$\sf{Length\;of\;the\;side \;of\; the\; triangle\; is\;13\:\dfrac{1}{3}\; cm.}$

Solution:

Given:

• Area of a square is 100 cm².
• Perimeter of the square is equal to the perimeter of an equilateral triangle.

To Find:

• Length of each side of the equilateral triangle = ??

How to find the answer:

To find the answer we first have to find the side of the square with an area of 100 cm². After finding the side of the square, we have to find the perimeter of the square. As it is given that, the perimeter of the square = perimeter of the triangle so, we can find the side of the triangle by dividing the perimeter by 3.

Step-by-Step Explanation:

Area of a square = (n)²

Where,

n = Side of the triangle

∴ (n)² = 100 cm²

$\sf{\implies n =\sqrt{100}\;cm}$

$\sf{\implies n = 10\;cm}$

Hence, length of the side of the square = 10 cm

Therefore, Perimeter of the square = 4n  (n = side of the square)

                                                           = (4 × 10) cm = 40 cm

Therefore, A/q

Perimeter of the triangle = Perimeter of the square = 40 cm

∵ Perimeter of the square = 40 cm

∴ Side of the triangle =  $\sf{\frac{Perimeter}{3}\; cm}$

$\sf{=\dfrac{40}{3}\; cm = 13\:\dfrac{1}{3}\; cm}$

$\sf{Hence, \:side \;of\; the\; triangle\; is\;13\:\dfrac{1}{3}\; cm.}$