Question

The area of the rhombus is 576 sq.cm and the length of one of its diagonal is half of the length of the other diagonal then find the length of the diagonals

Answer 1

Answer:-

Length of diagonals are :- 24 , 48 cm.

Given:-

Area = 576cm²

To find :-

The length of other diagonals.

Solution :-

Let the diagonals be $d_1 , d_2$

A/Q.

$d_1 = \dfrac{d_2}{2}$

Also, $2d_1 = d_2$

Now,

Area of Rhombus is given by :-

$\boxed{\sf{A = \dfrac{1}{2}\times d_1 \times d_2}}$

put the given value,

$576 = \dfrac{1}{2} d_1\times d_2$

$576 \times 2 = d_1 \times d_2$

$1152 = d_1 \times d_2$

Now,put the value of d2 .

$1152 = d_1 \times 2d_1$

$1152 = 2(d_1)^2$

$\dfrac{1152}{2}=2(d_1) ^2$

$576 = (d_1)^2$

$d_1 = \sqrt{576}$

$d_1 = 24 cm$

$d_2 = 2.d_1 \\d_2 = 2\times24$

$d_2 = 48cm$