Question

1. A piece of wire that is 28 inches long is cut into two pieces, each of which is then bent into the shape of a square. The larger square has side lengths that are three inches longer than the smaller square.

(a) If x is the side length of the smaller square and y is the side length of the larger square, write a system of equations that models this scenario.
(b) Solve the system of equations and determine the lengths of the two pieces of wire.

Answer 1

a)x+y=7 and y-x=3

b)x=2 and y=5

Explanation:

The total of the two perimeters must equal 28. That is:

4x+4y=28

x+y=7 (simplified)

The larger side length is 3 inches longer than the smaller side length. That is:

y=x+3

Sub 'x+3' in for y:

x+(x+3)=7

x+x=7-3

2x=4

x=2

y=x+3

=2+3

=5