Question

Area of rhombus is 216 sq cm its one diagonal is 24cm find length of its pther diagonal length of its side perimeter of rhombus

Answer 1

Let one diagonal of rhombus be x = 24 cm and other be y
Area of rhombus =
$\frac{1}{2} \times x \times y$
Therefore
$\frac{1}{2} \times 24 \times y = 216 \\ y = \frac{216}{12} \\ y = 18cm$
Therefore AC=18cm and BD=24cm
And diagonals of a rhombus bisect each other at right angles.
AO=18/2=9cm
BO=24/2=12cm
Let each side of rhombus be a cm
In right triangle ABO
By Pythagoras theorem,

AO^2 + BO^2 = AB^2
${9}^{2} + {12}^{2} = {a}^{2} \\ 81 + 144 = {a }^{2} \\ a = \sqrt{225} \\ a = 15cm$

Answer 2

The length of rhombus is 18 cm

Step-by-step explanation:

Let the other diagonal be x

Length of one rhombus = 24 cm

Area of rhombus =$\frac{1}{2} \times p \times q$

Area of rhombus =$\frac{1}{2} \times 24 \times x$

We are given that Area of rhombus is 216 sq cm

So,$\frac{1}{2} \times 24 \times x = 216$

$x=\frac{216 \times 2}{24}$

x=18

Hence The length of rhombus is 18 cm

#Learn more:

The diagonal of a rhombus is 16cm and 28cm.find the area of rhombus

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