Question

The ratio of the length of a rectangle to its breadth is 5:2 its area is 1690 cm?, find the perimeter of the rectangle. A) 182 B) 169 C) 196 D) 264​

Answer 1

ANSWER:

a) 182

STEP-BY-STEP EXPLANATION:

Given that the ratio of the length of a rectangle to its breadth is 5:2 and its area is 1690 cm².

We need to find out the perimeter of the rectangle.

Let's say the perimeter of rectangle be x.

Area of rectangle = length × breadth

Let's say that the length of the rectangle is 5x and breadth is 2x.

So,

$\implies\sf{1690\:=\:5x\:\times\:2x}$

$\implies\sf{1690\:=\:10x^{2}}$

$\implies\sf{ \cancel{\dfrac{1690}{10}}\:=\:x^{2}}$

$\implies\sf{169\:=\:x^{2}}$

$\implies\sf{\sqrt{169}\:=\:x}$

$\implies\sf{13\:=\:x}$

$\implies\sf{x\:=\:13}$

Therefore,

Length of rectangle = 5x = 5(13) = 65 cm

Breadth of rectangle = 2x = 2(13) = 26 cm

Now,

Perimeter of rectangle = 2(length + breadth)

Substitute the values in the above formula,

$\implies\sf{x\:=\:2(65+26)}$

$\implies\sf{x\:=\:2(91)}$

$\implies\sf{x\:=\:182}$

Therefore, the perimeter of the rectangle is 182 cm.