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 cm2. Find the length and
breadth of the rectangle.​

Answer 1

$\sf\large\green{\underline {given... }}$

Case (1) :- Breadth(b) is 4cm less than length(L)

Case (2) :- Length is increased by 4cam and breadth is decreased by 1cm.

• Area is increased by 40cm^2.

$\sf\large\green{\underline {to \: find... }}$

• Length and breadth.

$\sf\large\green{\underline {solution... }}$

Let length be (x)

Breadth is 4 less than length = (x - 4)

Area = (x)(x - 4)

$area = {x}^{2} - 4x$

Length is increased by 4cm...

• New length = (x+4)cm

Breadth is decreased by 1cm

• New breadth = (x - 5)cm

New Area ..

$= (x + 4)(x - 5) \\ = {x}^{2} - 5x + 4x - 20 \\ = {x}^{2} - x - 20$

We know, new area is incresed by 40cm^2.

So,

${x}^{2} - 4x = {x}^{2} - x - 20 - 40 \\ \\ - 4x + x = - 60 \\ \\ - 3x = 60 \\ \\ x = 20cm$

Therefore,

length = 20 cm

breadth = 16 cm

• .......breath = length - 4

Answer 2

Answer:

L=x+4=12cm

Length=12cm

Breadth=8cm

X=B=8cm

2(x+4)+2x=40

x=8

Thank you