Question

The perimeter of an equilateral triangle is 10 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. (Hint: An equilateral triangle has three sides the same length.)

Answer 1

14 inches

Explanation:

The side lengths of an equilateral triangle are the congruent.

The side lengths of a square are the congruent.

Let x be the length of one side of the equilateral triangle.

⇒ Perimeter of triangle = 3x

Let y be the length of one side of the square.

⇒ Perimeter square = 4y

Given:

• The perimeter of the triangle is 10 inches more than the perimeter of the square.
• The side of the triangle is 6 inches longer than the side of the square.

Create a system of equations with the given information and defined variables:

`\begin{cases}3x = 4y + 10\\x = y + 6\end{cases}`

Substitute the second equation into the first equation and solve for y:

`\implies 3(y+6)=4y+10`

`\implies 3y+18=4y+10`

`\implies 18=y+10`

`\implies y=8`

Therefore, the side length of the square is 8 inches.

Substitute the found value of y into the second equation and solve for x:

`\implies x=8+6`

`\implies x=14`

Therefore, the side length of the triangle is 14 inches.

Answer 2

• The side of the triangle is 14 in

======================

Let the sides be t for triangle and s for square.

Difference of perimeters

• 3t = 4s + 10

Difference of sides

• t = s + 6

Rearrange the second equation

• s = t - 6

Substitute this into first equation and solve for t

• 3t = 4s + 10
• 3t = 4(t - 6) + 10
• 3t = 4t - 24 + 10
• 3t = 4t - 14
• 4t - 3t = 14
• t = 14