Question

The area of a rhombus is 120 cm2. If one of its diagonals is of length 10 cm, then length of one of its sides is

Answer 1

Answer:-

Side = 13 cm

Given :-

A = 120 cm²

$d_1 = 10 cm$

To find :-

The length of the sides.

Solution:-

We know that area of rhombus is given by :-

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

Put the given value,

→$120 = \dfrac{1}{2} \times 10 \times d_2$

→$120 = 5d_2$

→$d_2 = \dfrac{120}{5}$

→$d_2 = 24cm$

We know that the diagonals of the rhombus bisect each other at 90°.

See attachment

See attachment Now,

→$OA = \dfrac{d_1}{2}$

→$OA = \dfrac{10}{2}$

→$OA = 5 cm$

→$OB = \dfrac{d_2 }{2}$

→$OB = \dfrac{24}{2}$

→$OB = 12 cm$

Now,

In $\triangle AOB , \angle{AOB}=90^{\circ}$

By using Pythagoras theorm,

→$AB ^2 = OA^2 + OB^2$

→$AB^2 = (5) ^2 + (12) ^2$

→$AB^2 = 25+ 144$

→$AB^2 = 169$

→$AB = \sqrt{169}$

→$AB = 13 cm$

hence,

The side of the rhombus will be 13 cm.

Answer 2

Answer:

The previous answer is correct i have checked it.