Question

The length of a rectangle is 6cm longer than the width. If the length is increased by 9cm and the width by 5cm, the perimeter will be 160cm. Find the dimensions of the original rectangle.

Answer 1

width: 30 cm, length: 36cm

Explanation:

Perimeter: 2w+2l

Rectangle 1: l=w+6

Rectangle 2: 2(w+5) + 2(l+9)=160

w+5 + l+9=80

w+l=66

w+w+6=66

w=30

l=36

Answer 2

• width: 30 cm
• length: 36 cm

Explanation:

Let w represent the width of the original rectangle in cm. Then its length is (w+6). The dimensions of the increased rectangle are ...

• length: (w+6) +9
• width: (w) +5

And the total of these new values is half the perimeter: 80.

(w +15) +(w +5) = 80

2w = 60 . . . . . . . . . . . . . subtract 20, collect terms

w = 30 . . . . . . . . . . . . . . divide by 2

The dimensions of the original rectangle are ...

• width: 30 cm
• length: 36 cm