Question

One diagonal of a rhombus is twice the other. If the area of the rhombus is 64 sq.cm then find the length of two diagonals.​

Answer 1

Let a be the side of a square and

b be the side of a rombus,and d1,d2 be the two diagonals of the rombus.

Given,

Area of square = Area of rombus

⇒a2=2d1d2

Also,

d1=2d2

∴a2=22d2d2

⇒a2=d2

⇒a=d2 and

⇒a=2d1

Area of rhombus is half of the product of the diagonals

2d1d2=64

⇒d1d2=128

⇒(2a)a=128

⇒a2=64

⇒a=8 cm

d1=2a=8×2

      =16 cm

d2

Answer 2

Solution :

$\bf{\blue{\underline{\underline{\bf{Given\::}}}}}$

One diagonal of a rhombus is twice the other. If the area of the rhombus is 64 cm².

$\bf{\blue{\underline{\underline{\bf{To\:find\::}}}}}$

The length of two diagonals.

$\bf{\blue{\underline{\underline{\bf{Explanation\::}}}}}$

Let the one diagonal of rhombus be 2r

Let the other diagonal of rhombus be r

A/q

Formula use :

$\bf{\boxed{\bf{Area\:of\:rhombus=\frac{1}{2} \times d_{1}\times d_{2}}}}}$

$\mapsto\sf{64cm^{2} =\dfrac{1}{2} \times 2r\times r}\\\\\mapsto\sf{64cm^{2} =\cancel{\dfrac{2}{2}} r\times r}\\\\\mapsto\sf{64cm^{2} =r^{2} }\\\\\mapsto\sf{\sqrt{64cm^{2} } =r}\\\\\mapsto\sf{\red{8cm=r}}$

Thus;

$\underline{\sf{The\:one\:diagonal\:of\:rhombus\:=d_{1}=2r=2(8cm)=\pink{16cm}}}\\\underline{\sf{The\:other\:diagonal\:of\:rhombus\:=d_{2}=r=\pink{8cm}}}$