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 6 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 \((x + 16)\) centimeters.
The perimeter of the square \(P_{square}=4x\) and the perimeter of the equilateral triangle \(P_{triangle}=3(x + 16)\).
Since the perimeters are equal, we have the equation \(4x=3(x + 16)\).
Expand the right - hand side: \(4x = 3x+48\).
Subtract \(3x\) from both sides: \(4x-3x=3x + 48-3x\), so \(x = 48\).
The length of a side of the square frame is 48 centimeters.