Simultaneous Equations

Question

The perimeter of a rectangle is 14m. If the length is doubled and the width is halved the new perimeter is 22m. By using a pair of simultaneous equations determine the length and width of the rectangle.

Answer 1

2L + 2w = 14 ---> L+W=7

2(2L) + 2(1/2w) = 22

4L + w = 22

L + w = 7

4L + w = 22

subtracts Eq #2 MINUS Eq #1:

3L = 15

L=5

length is 5, width is 2.