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.