Question

The area of a rhombus is 480 cm², and one of its diagonals measures 48 cm. Find (i) the length of the other diagonal, (ii) the length of each of its sides, and (iii) its perimeter.

Answer 1

It is given that,
Area of rhombus = 480 cm².
One of the diagonal = 48 cm.

(i) Area of the rhombus = $\frac{1}{2}\times d_1\times d_2$
$$\begin{gathered} \Rightarrow 480=\frac{1}{2}\times 48\times d_2 \\ \Rightarrow 480=24\times d_2 \\ \Rightarrow d_2=\frac{480}{24} \\ \Rightarrow d_2=20\mathrm{cm} \end{gathered}$$

Hence, the length of the other diagonal is 20 cm.

(ii) We know that the diagonals of the rhombus bisect each other at right angles.



In right angled ∆ABO,
AB² = AO² + OB² (Pythagoras Theorem)
⇒ AB² = 24² + 10²
⇒ AB² = 576 + 100
⇒ AB² = 676
⇒ AB = 26 cm

Hence, the length of each of the sides of the rhombus is 26 cm.

(iii) Perimeter of the rhombus = 4 × side
= 4 × 26
= 104 cm

Hence, the perimeter of the rhombus is 104 cm.