Question

A rhombus has diagonals of length $a$ and ($a$+$\sqrt{a}$) units. If the area of the rhombus is $12$, then $a$ equals to

• A. $2$
• B. $3$
• C. $4$
• D. $9$

Answer 1

Answer: (C)

$4$

Area of rhombus$=\frac{productofdiagonals}{2}$

$12=\frac{a(a+\sqrt{a})}{2}$

$a(a+\sqrt{a})=24$

Solving the equation

Only factor of $24$ such that is square root is an integer is $4$

$4(4+\sqrt{4})$

$\to 24$

Hence $a=4$