Question

A square and an equilateral triangle have equal perimeters. If the square has sides of length 3, what is the length of one side of the triangle?​

Answer 1

Solution!!

A square and an equilateral triangle have equal perimeters. The square has sides of length 3.

First let's calculate the perimeter of the square,

Perimeter of square = 4a

Where 'a' denotes the length of side of the square.

`\rm Perimeter_((square)) = 4 * 3`

`\rm Perimeter_((square)) = 12`

Since the square and an equilateral triangle have equal perimeters. So, The perimeter of the triangle will also be 12.

Perimeter of the triangle is equal to the sum of each side of the triangle.

Perimeter of triangle = a + a + a

Here 'a' denotes the sides of triangle.

`\rm 12 = a + a + a`

`\rm 12 = 3a`

Divide both sides by 3,

`\rm a = 4`

Hence, The length of one side of the triangle is 4.