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

Answer:

Length=15

Breadth=12

Step-by-step explanation:

let length be ...x

breadth be...x-3

A to Q

(x+2)×(x-3+2)=(x)×(x-3)+58

(x+2)×(x-1)=x^2 - 3x + 58

x^2 + x - 2=x^2 -3x+58

4x=58+2

4x = 60

x=15

length=15

breadth=12

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Answer 2

$\huge\sf\pink{Answer}$

☞ Length = 15 cm

☞ Breath = 12 cm

$\rule{110}1$

$\huge\sf\blue{Given}$

➳ 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.

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

➢ Length and breadth of the rectangle?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Assuming,

❍ 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

As per the question,

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

➳ Breadth of the new rectangle = (x+2) cm.

➳ $\sf Area \:of \:the\: new \:rectangle\: =\: (x+5)(x+2) c{m}^{2}$

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

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

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

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

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

$\leadsto\sf\green{x=12}$

$\bullet\sf\red{\;Breadth \:= \:12\: cm}$

$\sf\bullet\red{\;Length\: = \:(12+3)\: =\: 15 \:cm}$

$\rule{170}3$