Question

Part 1

The perimeter of an equilateral triangle is 4 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.​ (Hint: An equilateral triangle has three sides the same​ length.)

Answer 1

12 inches

Explanation:

You want the side length of an equilateral triangle if the perimeter of the triangle is 4 inches more than the perimeter of a​ square, and the side of the triangle is 4 inches longer than the side of the square.

Setup

Let t represent the side length of the triangle. Then 3t is perimeter of the triangle, and 3t -4 is the perimeter of the square. The side length of the square is 1/4 of this, so we have ...

(3t -4)/4 +4 = t

Solution

3/4t -1 +4 = t . . . . . eliminate parentheses

3 = 1/4t . . . . . . . . . subtract 3/4t, combine terms

12 = t . . . . . . . . . . . multiply by 4

The side length of the triangle is 12 inches.

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Additional comment

The perimeter of the triangle is 36 inches, so the perimeter of the square is 32 inches. The side length of the square is 8 inches, 4 inches less than the side length of the triangle.

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