Question

The perimeter of an equilateral triangle is 15 inches more than the perimeter of a​ square, and the side of the triangle is 8 inches longer than the side of the square. Find the side of the triangle.​

Answer 1

The length of a side of the triangle is 17 inches.

SOLUTION:

Given, the perimeter of an equilateral triangle is 15 inches more than the perimeter of square.

And the side of the triangle is 8 inches longer than the side of the square.

Let the length of the side of a triangle be x.

And the length of the side of a square be y.

perimeter of triangle = a + b + c , where a , b, c represents side

perimeter of square = a + a + a +a , where a represents side

Given, the perimeter of an equilateral triangle is 15 inches more than the perimeter of square. Hence we form a equation as

Then, x + x + x = 15 + y + y + y + y

3x = 15 + 4y ---- (1)

Now, given that, x = 8 + y ---- (2)

Substitute (2) in (1)

3(8 + y) = 15 + 4y

24 + 3y = 15 + 4y

4y – 3y = 24 – 15

y = 9

Now, substitute y value in (2)

x = 8 + 9 = 17

Hence, the length of a side of the triangle is 17 inches.