Question

A square is changed into a pentagon by building an equilateral triangle on top of it, as shown. By what percent does the perimeter increase going from the square to the pentagon?

Answer 1

Answer: The perimeter is going to increase 25% from the square to the pentagon.

Step-by-step explanation:

• A square is a quadrilateral having its all sides equal.
• A equilateral triangle is a triangle that has equal sides.

Let the side of the given square be x.

Perimeter of square =4x

If a square is changed into a pentagon by building an equilateral triangle on top of it , Then the base of equilateral triangle will occupy the same side-length as that of square.

Thus , the pentagon will become a regular pentagon having all its sides equal.

Perimeter of pentagon = 5(side)= 5x

Increase in perimeter = Perimeter of pentagon- Perimeter of square

= 5x-4x= x

Now , the percent increase in perimeter = $\dfrac{\text{Increase in perimeter}}{\text{Perimeter of square}}\times100$

$=\dfrac{x}{4x}\times100\\\\ =\dfrac{100}{4}=25\%$

Hence, the perimeter is going to increase 25% from the square to the pentagon.