Question

The length of a rectangle is greater than the breadth by 18 cm. if both length and breadth are increase by 6 cm. then area increase by 168 cm2. find the length and breath of the rectangle.

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Answer 1

Answer:

Question

• The length of a rectangle is greater than the breadth by 18 cm. if both length and breadth are increase by 6 cm, then area increased by 168 cm2. Find the length and breath of the rectangle.

Answer

Given :-

• The length of a rectangle is greater than the breadth by 18 cm. if both length and breadth are increased by 6 cm. then area increase by 168 cm2.

To Find :

• Breadth and Length of Rectangle.

Solution :

$\longmapsto\tt{Let \: Breadth =x \: \:cm}$

$\longmapsto\tt{Let \: Length= \: (x + 18)\:cm}$

■ Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

$\longmapsto\tt{Area \: = x(x + 18)}$

■ According to statement,

If length and breadth increased by 6 cm, the area increases by 168.

So, new dimensions are as follow :

$\longmapsto\tt{Breadth =x + 6}$

$\longmapsto\tt{Length=x + 24}$

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

$\longmapsto\tt{Area = (x + 6)(x + 24)}$

■ According to statement,

$\small \bf(x + 6)(x + 24) = x(x + 18) + 168$

$\small \bf {x}^{2} + 6x + 24x + 144 = {x}^{2} + 18x + 168$

$\bf \implies \:30x + 144 = 18x + 168$

$\bf \implies \:30x - 18x = 168 - 144$

$\bf \implies \:12x = 24$

$\bf \implies \:x = 2 \: cm$

So,

Breadth = 2 cm

Length = 2 + 18 = 20 cm

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