rectangle is 4cm longer than it is wide.

Question

if both the length and the breadth are increased by 1cm, the area would be increased by 18cm. Find the length and the breadth of the rectangle

Answer 1

Length is 4 cm longer than width:

L = w + 4

Increasing L &W both by 1 increases area by 18:

(L+1)(w+1) = LW + 18

 

(w+4+1)(w+1) = w(w+4)+18

(w+5)(w+1) = w²+4w+18

w² + 6w + 5 = w² + 4w + 18

6w + 5 = 4w + 18

2w = 13

w = 6.5

L = w+4 = 10.5

 

The rectangle is 10.5 cm by 6.5 cm