Question

Could someone please help me with this Math problem, Thank you.

The Dig It Project is designing two gardens that have the same perimeter. One garden is a trapezoid whose nonparallel sides are equal. The other is a quadrilateral. Two possible designs are shown at the right?

Based on these designs, is there more than one value for x? Explain how you know this.

Answer 1

To find the perimeters, all we need to do is add the sides together.

Top garden: (2x-2) + (x+1) + (x) + (x+1) = 5x

Bottom garden: (2x-9) + (x+1) + (x+8) + (x) = 5x

If the perimeters are the same, we can set them equal to each other.

5x = 5x

No matter what x is equal to, the perimeters will be equal, so yes there is more than one value for x.