Question

two frames are needed with the same perimeter, one frame in the shape of a square and one in the shape of an equilateral triangle. each side of the triangle is 18 centimeters longer than each side of the square. find the length of a side of each frame. (an equilateral triangle has sides that are the same length.) the length of a side of the square frame is

Explanation:

Answer:

Let the side - length of the square be \(x\) centimeters. Then the side - length of the equilateral triangle is \((x + 18)\) centimeters.
The perimeter of the square \(P_{square}=4x\) and the perimeter of the equilateral triangle \(P_{triangle}=3(x + 18)\).
Since the perimeters are equal, we have the equation \(4x=3(x + 18)\).
Expand the right - hand side: \(4x=3x+54\).
Subtract \(3x\) from both sides: \(4x−3x=3x + 54−3x\), so \(x = 54\).
The side - length of the equilateral triangle is \(x + 18=54+18 = 72\) centimeters.
The length of a side of the square frame is 54 centimeters.
The length of a side of the equilateral - triangle frame is 72 centimeters.