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.

Answer 1

..let x be the side of the square garden, (x+1) the side of the equilateral triangle garden

square garden perimeter = x*4 = 4x

equilateral triangle garden perimeter = 3(x+1)= 3x+3

the 2 gardens have the same perimeter

4x=3x+3

we solve the equation to find the value of x

4x=3x+3

4x-3x=3

x=3

square garden side: 3m

garden side equilateral triangle: 3+1=4m