Question

The area of a rhombus is 119 cm² and its perimeter is 56 cm. The height of the rhombus is

(a) 7.5 cm (b) 6.5 cm (c) 8.5 cm (d) 9.5 cm

Answer 1

Let b the side of the rhombus and h be its height.
Perimeter of rhombus = 56 cm
$$\begin{gathered} \Rightarrow 4b=56 \\ \Rightarrow b=14\mathrm{cm} \end{gathered}$$
Now
Area of rhombus = 119 cm²
$$\begin{gathered} \Rightarrow b\times h=119 \\ \Rightarrow 14\times h=119 \\ \Rightarrow h=\frac{17}{2}=8.5\mathrm{cm} \end{gathered}$$
Hence, the correct option is (c).