Question

Lengths of the diagonals of a rhombus are 10 units and (7x + 3) units. If its area is $120c{m}^2$, find x.

• A. 3

Answer 1

The correct option is A 3

Given: Area of the rhombus = 120 cm²
Length of one diagonal = 10 units
Length of the other diagonal = (7x + 3) units

Area of a rhombus = $\frac{1}{2}$$\times$(product of diagonals)

$\Rightarrow 120=\frac{1}{2}\times 10\times (7x+3)$

$\Rightarrow 120=5\times (7x+3)$

$\Rightarrow (7x+3)=\frac{120}{5}=24$

$\Rightarrow 7x=21$

$\Rightarrow x=3$

Therefore, the value of x is 3 units.