Question

The area of a rectangle gets reduced by 80 if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units. The area is incraesed by 50 units. Find the length and breadth of the rectangle ?

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Length = p

Breadth = n

Area = p × n

So,

(p - 5)(n + 2) = pn - 80

2p - 5n + 70 = 0 ..... (1)

Also,

(p + 10)(n - 5) - pn = 50

5p + 10n = 100

p - 2n + 20 = 0 ....... (2)

Multiply (2) by 2 we get :-

2p - 4n = -40 ........ (3)

Subtracting (3) from (1)

-n = -30

n = 30

${\boxed{\sf\:{Substitute\;the\;value\;in\;(1)}}}$

2p - 5(30) = -70

2p = -70 + 150

2p = 80

$\tt{\rightarrow p=\dfrac{80}{2}}$

p = 40

${\boxed{\sf\:{Length=\;40\;and\;Breadth=\;30}}}$