Question

The sides of a rhombus are $5$cm and one diagonal is $8$ cm. Calculate

(i) the length of the other diagonal and

(ii) the area of the rhombus.

Answer 1

Diagonals bisect each other and they are perpendicular in rhombus

Let half the length of second diagonal be x

As two diagonals and a side form right angled triangle ;

$\Rightarrow x^2+4^2=5^2$

$\Rightarrow x=3$

$\Rightarrow$length of 2nd side $=2x=6$cm

Area of rhombus $=\frac{1}{2}{d}_1{d}_2$

$=\frac{1}{2}\times 8\times 6$

$=24c{m}^2$