Question

Let the width of rectangle MATH equal w. The length of the rectangle is 3cm longer than the width. In rectangle GEOM the width is 1 more than w and the length is 5 less than twice w. If their perimeters are equal, find w.

Answer 1

7 cm

Explanation:

The perimeter P of a rectangle is given as

p = 2 (l + b) where l and b are the length and width respectively

hence for a rectangle where the length of the rectangle is 3cm longer than the width w

the perimeter

= 2 (w + 3 + w)

= 2(2w + 3)

In another rectangle where the width is 1 more than w and the length is 5 less than twice w, the perimeter

= 2(2w - 5 + w +1)

= 2 (3w - 4)

since the perimeters are equal, equate both equations

2(2w + 3) = 2 (3w - 4)

2w + 3 = 3w -4

collect like terms

3w - 2w = 4 + 3

w = 7cm