Question

Claire purchased just enough fencing to border either a rectangular or triangular garden, as shown, whose perimeters are the same. M8 PotW 12 garden.PNG How many feet of fencing did she buy? Show your process and explain your answer. Please Helppp!

Answer 1

Perimeter of the rectangle = length + length + width + width
P = (3x-3) + (3x-3) + (x-3) + (x-3)
P = 3x + 3x + x + x - 3 - 3 - 3 - 3
P = 8x - 12

Perimeter of the triangle = side 1 + side 2 + side 3
P = (2x-1) + (2x-1) + (2x)
P = 2x + 2x + 2x - 1 - 1
P = 6x - 2

The perimeter is equal for both shapes
6x - 2 = 8x - 12
-2 + 12 = 8x - 6x
10 = 2x
x = 10÷2
x = 5

The length of fencing needs to be bought for each shape is (use either expression of perimeter to work it out)

P = 6x - 2 = 6(5) - 2 = 30 - 2 = 28 feet