Question

The length and breadth of a rectangle are in the ratio 7: 4. If the length is doubled and the breadth is increased by 6 cm, the ration of the length and breadth becomes 2 : 1. Find the length and breadth of the rectangle.​

Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The length and breadth of a rectangle are in the ratio 7: 4.

So, Let assume that

↝ Length of rectangle = 7x cm

↝ Breadth of rectangle = 4x cm

So,

$\red{\begin{gathered}\begin{gathered}\rm :\longmapsto\:\begin{cases} &\sf{Length \: of \: rectangle = 7x} \\ \\ &\sf{Breadth \: of \: rectangle = 4x} \end{cases}\end{gathered}\end{gathered}}$

According to statement,

If the length is doubled and the breadth is increased by 6 cm, the ratio of the length and breadth becomes 2 : 1.

So,

Length of rectangle = 2 × 7x = 14x cm

Breadth of rectangle = 4x + 6 cm

So,

$\rm :\longmapsto\:\dfrac{14x}{4x +6 } = \dfrac{2}{1}$

$\rm :\longmapsto\:14x = 8x + 12$

$\rm :\longmapsto\:14x - 8x = 12$

$\rm :\longmapsto\:6x = 12$

$\bf\implies \:x = 2$

Hence,

$\red{\begin{gathered}\begin{gathered}\rm :\longmapsto\:\begin{cases} &\sf{Length \: of \: rectangle = 7x = 14 \: cm} \\ \\ &\sf{Breadth \: of \: rectangle = 4x = 8 \: cm} \end{cases}\end{gathered}\end{gathered}}$