Question

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Answer 1

Let the length of the other diagonal of the rhombus be $x$.
A rhombus is a special case of a parallelogram.
The area of a parallelogram is given by the product of its base and height.
Thus, area of the given rhombus = Base × Height
= 6 cm × 4 cm
= 24 cm2

Also, area of rhombus = $\frac{1}{2}$ (Product of its diagonals)
24 = $\frac{1}{2} (x × 8$ cm$)$
$x × 4 = 24$
$x = 6$ cm

Thus, the length of the other diagonal is 6 cm.