Question

Two gardens are being fenced in. Both gardens will require the same amount of fencing​ (both gardens have the same perimeter in​ meters). One garden is in the shape of a square and the other is in the shape of an equilateral triangle. Each side of the triangle is 1 meter longer than each side of the square. Find the dimensions of the garden.

​square: ____ m on each side
​triangle: _____ m on each side

Answer 1

square - 3m on each side

triangle- 4m on each side

Explanation:

4*l=3(l+1)

4l = 3l+3

-3l -3l

l= 3m

Answer 2

square: 3 m on each side

triangle: 4 m on each side

Explanation:

Suppose the length of the square is called x meter.

Then the perimeter of that square garden is 2 times the length and 2 times the width = 2x + 2x = 4x

So perimeter square garden = 4*(x)

Given

1. The length of the side of the equilateral triangle = x+1

Then the perimeter of the equilateral triangle is 3 times x+1 = 3*(x + 1) = 3x + 3

So perimeter equilateral triangle garden = 3*(x) + 3

Given

2. Both gardens have the same perimeter.

perimeter square garden = 4x

perimeter equilateral triangle garden = 3x + 3

Combine these two pieces of information:

4x = 3x + 3

4x -3x = 3

x = 3

Since the length of the square was called x meter, we now know that one side of the square must be 3m.

square: 3 m on each side.

Since length of the side of the triangle = x+1, we now know that one side of the triangle garden = 3 +1 = 4m.

triangle: 4 m on each side.