Question

If length of a diagonal of rhombus is 30 cm ahd its 240sq cm find it perimeter​

Answer 1

Here is your answer..........

Answer 2

If length of a diagonal of rhombus is 30 cm ahd its 240sq cm find it perimeter

Solution:

We know that Area of Rhombus =1/2 diagonal 1 × diagonal 2

d1 =30 cm

Area = 240 sq-cm

$240 = \frac{1}{2}\times 30 \times d_2 \\ \\ d_2 = \frac{240\times 2}{30} \\ \\ d_2 = 16 \: cm$

We know that Diagonal of rhombus bisect each other at 90°,and it has all sides equal.

So, apply Pythagoras Theorem for one right triangle

B= 15 cm

P= 8 cm

$H=\sqrt{ {B}^{2} + {P}^{2} } \\ \\ = \sqrt{( {15)}^{2} + ( {8)}^{2} } \\ \\ = \sqrt{225 + 64} \\ \\ = \sqrt{289} \\ \\ = 17 \: cm$

So all sides of Rhombus are 17 cm

Perimeter= 4 × side

$= 4 \times 17 \\ \\ = 68 \: cm$

Hope it helps you.