Question

The area of a rhombus is 106 cm2 and one of its diagonals is 20 cm, calculate its perimeter.​

Answer 1

Area of rhombus =  $\frac{pq}{2}$ where p and q are the diagonals

So,

$\frac{20q}{2} = 106$

$10q = 106$

$q = \frac{106}{10}$

$q = 10.6$
Now, $s^2 = (\frac{p}{2})^2 + (\frac{q}{2})^2$

So,

$s^2 = (\frac{20}{2})^2 + (\frac{10.6}{2})^2$

$s^2 = 10^2 + 5.3^2$

[tex]s^2 = 100 + 28.09\\ s^2 = 128.09\\ s = \sqrt{128.09}[/tex]

So, perimeter:

$4s = 4*\sqrt{128.09} = 4\sqrt{128.09}$

This value is roughly equal to 45.5 cm