Question

Sammie bought just enough fencing to border either a rectangular plot or a square plot, as shown. The perimeters of the plots are the same.How many meters of fencing did she buy?

Answer 1

Perimeter of square : p = 4a.....
p = 4(x + 2)
p = 4x + 8

perimeter of rectangle : p = 2(L + W)
p = 2(3x + 2 + x - 1)
p = 2(4x + 1)
p = 8x + 2

so if the perimeters are te same, lets set them equal to each other and solve for x

4x + 8 = 8x + 2
8 - 2 = 8x - 4x
6 = 4x
6/4 = x
1.5 = x

the square : p = 4x + 8.....p = 4(1.5) + 8.....p = 14 meters
the rectangle : p = 8x + 2....p = 8(1.5) + 2.....p = 14 meters

so she bought 14 meters of fencing <==