Question

The breadth of a rectangle is 4 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 ^2. Find the length and breadth of the rectangle .​

Answer 1

$\green{\bf Solution }$

$\pink{\sf Let \: the \: length \: of \: Rectangle \: be \: x}$

$\pink{\sf Therefore, \: Breadth \: be \: x - 4}$

So, finding area of the rectangle.

$\dag \: \bf Area = length \times breadth \: \dag$

$\tt \implies (x) \times (x-4)$

$\tt \implies x^{2} - 4x$

Now, According to Question

$\sf \implies (x+4)(x - 4 - 1) = ( {x}^{2} - 4x ) + 40 \\ \\ \sf \implies \cancel{{x}^{2}} \cancel{ - 4x} - x \cancel{+ 4x }- 16 - 4 = \cancel{x^{2} } - 4x + 40 \\ \\ \sf \implies - x - 20 = - 4x + 40 \\ \\ \sf \implies - x + 4x = 40 + 20 \\ \\ \sf \implies \: 3 x = 60 \: \\ \\ \sf \implies \cancel\dfrac{60}{20} \\ \\ \sf \implies20$

$\purple{\sf Therefore, x = 20}$

$\red{ \bf {\dag \: Length \longrightarrow x = 20 \: \dag}}$

$\red {\bf{\dag Breadth \longrightarrow x - 4 = 20 - 4 = 16 \: \dag}}$

Answer 2

$\bf{\red{Answer}}$

Let the Breadth be x

So, according to question, length will be x + 4

Now, we have length & breadth

So, we can simply find Area

Area = length × Breadth

$\rm \implies (x + 4) \times (x)$

$\rm \implies x^2 + 4x$

So, now we simply put up the values According to the Question

So,

$\rm \implies(x - 1) (x + 4 + 4) = x^2 + 4x + 40$

$\rm \implies(x-1)(x+8) = x^2 + 4x + 40$

$\rm \implies\cancel {x^2} - x + 8x - 8 = \cancel{x^2} + 4x + 40$

$\rm \implies 7x - 8 = 4x + 40$

$\rm \implies 7x - 4x = 40 + 8$

$\rm \implies 3x = 48$

$\rm \implies x = 16$

$\boxed{\underline{\bf{\pink{Breadth = 16 cm}}}}$

$\boxed{\underline{\bf{\pink{Length = 16 + 4 = 20 cm}}}}$