Question

The length of a rectangle is 7 m less than twice the width. If the length is decreased by 1 m and the width by 4 m, the perimeter will be 66 m. Find the dimensions of the original rectangle.

Answer 1

Let the width be x m, then the length is 2x-7 m.

If the length is decreased by 1m, then new length is 2x-7-1=2x-8 m.

If the width is decreased by 4 m, then new width is x-4 m.

Find the perimeter of new recangle:

$P_{new}=2x-8+x-4+2x-8+x-4=6x-24.$

The perimeter of new rectangle is 66 m, then

$6x-24=66,\\\\6x=66+24,\\\\6x=90,\\\\x=15.$

Therefore, old width was 15 metres and old length was 2·15-7=23 metres.

Answer: original width: 15 metres, original length: 23 metres