Question

The area of a rhombus is 144 sq.m & one of its diagonal is double the other. Find the length of the diagonals. ​

Answer 1

Given :

• Area of Rhombus is 144 m².
• One of its Diagonal is double of the other.

To Find :

• Length of the diagonals of Rhombus.

Solution :

$\longmapsto\tt{Let\:{d}_{1}=x}$

As Given that other diagonal is double of first .So ,

$\longmapsto\tt{{d}_{2}=2x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rhombus=\dfrac{1}{2}\times{{d}_{1}}\times{{d}_{2}}}$

Putting Values :

$\longmapsto\tt{144=\dfrac{1}{2}\times{x}\times{2x}}$

$\longmapsto\tt{144\times{2}=2{x}^{2}}$

$\longmapsto\tt{288={2x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{288}{2}={x}^{2}}$

$\longmapsto\tt{\sqrt{144}=x}$

$\longmapsto\tt\bf{x=12}$

Value of x is 12..

Therefore :

$\longmapsto\tt{1\:Diagonal\:of\:Rhombus=x}$

$\longmapsto\tt\bf{12m}$

$\longmapsto\tt{2\:Diagonal\:of\:Rhombus=2(12)}$

$\longmapsto\tt\bf{24m}$