Question

The perimeter of an equilateral triangle is 11 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. find the side of the triangle.

Answer 1

Answer:

13 inches

Step-by-step explanation:

Let P(t) and P(s) be the perimeters of the equilateral triangle and square respectively. Similarly, t and s be the side lengths of equilateral triangle and square respectively.

According to the first condition :

(Perimeter of an equilateral triangle is 11 inches more than the perimeter of a square)

$\implies P(t) = P(s) + 11$

$\implies 3t = 4s + 11....(1)$

According to the second condition :

(The side of the triangle is 6 inches longer than the side of the square)

$\implies t = s + 6....(2)$

From equations (1) & (2)

3(s + 6) = 4s + 11

3s + 18 = 4s + 11

3s - 4s = 11 - 18

-s = - 7

s = 7 inches

$\because t = s + 6$

$\because t = 7 + 6$

$\because t = 13\: inches$

Thus the side of the triangle is 13 inches long.