Question

The breadth of a rectangle is 4 cm less than its length. If the length is increased by 4 cm and the
breadth is decreased by 1 cm, the area of the rectangle is increased by 40 cm. Find the length ano
breadth of the rectangle.​

Answer 1

Let the length be L cm

Therefore, Breadth will be (1 - 4) cm

Now, we know that,

Area of rectangle = length × Breadth

=> A = L(L - 4)

Now,

According to question,

Length is increased by 4 cm

=> New length, L' = (L + 4) cm

Breadth is decreased by 1 cm

=> New breadth = (L - 5) cm

Also, Area increased by 40 sq. cm

=> New area = (A + 40) sq. cm

=> A' = A + 40

=> (L + 4) (L - 5) = L(L - 4) + 40

Therefore, we will get,

=> L² - 5L + 4L - 20 = L² - 4L + 40

=> - L - 20 = - 41 + 40

=> 4L - L = 40 + 20

=> 3L = 60

=> L = 60

3

=> L = 20

Therefore, length = 20 cm

Thus, Breadth = 20 - 4 = 16 cm

Hence, the required length is 20cm and breadth is 16 cm.