Question

Only for scholars please tell me answer of this question in easy way but Step-by-step
the perimeter of a rhombus is 52 cm and length of one of its diagonal is 24 cm find the area of the Rhombus

Answer 1

Answer : 120 cm²

Solution :
________

Given that : Perimeter of rhombus = 52 cm

As we know that : Perimeter of rhombus = 4a

Now, according to the question :

4a = 52

=> a = 13 cm

By the Pythagoras theoram :

${(side)}^{2} = ( {\frac{d1}{2}})^{2} +( { \frac{d2}{2} })^{2} \\ \\ = > {(13)}^{2} = ({ \frac{24}{2} })^{2} + {( \frac{d2}{2} })^{2} \\ \\ = > 169 = 144 + ({ \frac{d2}{2} })^{2} \\ = > 5 = \frac{d2}{2} \\ \\ = > d2 = 10 \: cm \:$

So, the length of other diagonal will be 10 cm.

Now, Area of rhombus :

$\frac{1}{2} \times (d1 \times d2) \\ \\ = > \frac{1}{2} \times 10 \times 24 \\ \\ = > 120 \: {cm}^{2}$

So, the area of rhombus will be 120 cm²