how to do this?

Question

Claire bought just enough fencing to enclose either a rectangular garden or a triangular garden, as shown. The two gardens have the same perimeter. How many feet of fencing did she buy?

 

(4x − 4)		(3x − 1)	(3x − 1)	3x
	(x − 4)

 

Claire bought 

 feet of fencing.

Answer 1

Hard to tell about the dimensions of the rectangle and triangle, but I assumed that the sides of the rectangle are 4x - 4 and x - 4 and the triangle has two sides of 3x - 1 and a side = 3x.

If that's the case, and the perimeters are equal, then 2(4x - 4) + 2(x - 4) = 2(3x - 1) + 3x.

Simplifying; 8x - 8 + 2x - 8 = 6x - 2 + 3x -> 10x - 16 = 9x - 2

Solving for x gives x = 14

Substituting into each of the perimeter equations gives a perimeter for each of 124.