Question

The perimeter of an equilateral triangle is 6 inches more than the perimeter of a square, and the side of the triangle is 4 inches longer than the side of the square. Find the side of the triangle

Answer 1

The length of the side of the triangle is 10 inches.

Explanation:

Let p = perimeter of the equilateral triangle

Let P = perimeter of the square

Let s = length of side of the triangle

Let S = length of side of the square

"The perimeter of an equilateral triangle is 6 inches more than the perimeter of a square"

p = P + 6 Equation 1

"the side of the triangle is 4 inches longer than the side of the square"

s = S + 4 Equation 2

We have 2 equations and 4 unknowns. We need two more equations. We use the definition of perimeter to get the other two equations.

For an equilateral triangle,

p = 3s Equation 3

For a square,

P = 4S Equation 4

Substitute p and P of Equation 1 with equations 3 and 4. Then write equation 2.

3s + 4S = 6

s = S + 4

Now we have a system of 2 equations in 2 unknowns. We can solve for s and S. We can use the substitution method. Solve the second equation for S.

S = 4 - s

Substitute S = 4 - s into equation 3s + 4S = 6.

3s + 4(4 - s) = 6

3s + 16 - 4s = 6

-s = -10

s = 10

Answer: The length of the side of the triangle is 10 inches.