Question

the length of a rectangle exceeds it's breadth by 3 cm . If each the length and breadth are increased by2 cm , the area of the new rectangle will be 58 cm^2 more than that of the given rectangle. find the length and breadth of the given rectangle

Answer 1

Given :

• The length of a rectangle exceeds it's breadth by 3 cm.
• Each the length and breadth are increased by 2 cm , the area of the new rectangle will be 58 cm² more than that of the given rectangle.

To find :

• Length and breadth of the given rectangle.

Solution :

Consider,

• Breadth of the given rectangle = x cm

Then,

• Length of the given rectangle = (x+3) cm

Area of the given rectangle ,

= x(x+3) cm²

= (x²+3x) cm²

According to the question ,

• Each the length and breadth are increased by 2 cm , the area of the new rectangle will be 58 cm² more than that of the given rectangle.

Therefore,

• Length of the new rectangle= (x+3+2) = (x+5) cm.
• Breadth of the new rectangle = (x+2) cm.

Area of the new rectangle,

=(x+5)(x+2) cm²

$\implies\sf{(x+5)(x+2)=x^2+3x+58}$

$\implies\sf{x^2+2x+5x+10=x^2+3x+58}$

$\implies\sf{7x+10=3x+58}$

$\implies\sf{7x-3x=58-10}$

$\implies\sf{4x=48}$

$\implies\sf{x=12}$

• Breadth = 12 cm.
• Length = (12+3) = 15 cm.

Therefore, the length of the given rectangle is 15 cm and the breadth of the given rectangle is 12 cm.

Answer 2

${\underline{\sf{Question}}}$

the length of a rectangle exceeds it's breadth by 3 cm . If each the length and breadth are increased by 2 cm , the area of the new rectangle will be 58 cm² more than that of the given rectangle. find the length and breadth of the given rectangle.

${\underline{\sf{Solution}}}$

Let the breadth(b) of a reactangle be xcm

⇒ Length of a rectangle ,l = x+3 cm

Area of a rectangle

A = l×b

= length × breadth

= x(x+3)= x²+3x

If the length and breadth are increased by 2 cm .

l' = l+2 = (x+5)

and b ' = b+2 = (x+2) cm

Area of new Rectangle

A' = l' × b'

= (x+5)(x+2)

According to the question :

Area of new Rectangle = Area of initial Rectangle + 58 cm²

$\sf \implies(x + 5)(x + 2) = x {}^{2} + 3x + 58$

$\sf \implies \: x {}^{2} + 7x + 10 = x {}^{2} + 3x + 58$

$\sf \implies \: 7x - 3x = 58 - 10$

$\sf \implies \: 4x = 48$

$\sf \implies \: x = 12$

Therefore,

The length of Rectangle = x+3 = 15 cm

The breadth of Rectangle = x= 12 cm

$\rule{200}2$

Verification :

Length = 15

breadth = 12

⇒ Area = 15× 12 = 180 cm²

If each the length and breadth are increased by 2 cm , the area of the new rectangle will be 58 cm² more than that of the given rectangle.

⇒ Area of new rectangle = area of initial Rectangle + 58

17× 14 = 180+58

238= 238

Hence verified !