The length of one of the diagonals of a rhombus is 48 cm. If the side of the rhombus is 26 cm, then what is the area of the rhombus?

Let's assume that each side of the rhombus is 'a'.

The diagonals of a rhombus are P and Q.

The length of one of the diagonals of a rhombus is 48 cm.

P = 48 cm

If the side of the rhombus is 26 cm.

a = 26 cm

So as per the Pythagoras theorem, $$a^2\ =\ \left(\frac{P}{2}\right)^2+\left(\frac{Q}{2}\right)^2$$

$$26^2\ =\ \left(\frac{48}{2}\right)^2+\left(\frac{Q}{2}\right)^2$$

$$676 = 576+\frac{Q^2}{4}$$

$$\frac{Q^2}{4} = 676-576 = 100$$

$$Q^2 = 400$$

Q = 20 cm

Area of the rhombus = $$\frac{PQ}{2}$$

= $$\frac{48\times20}{2}$$

= $$48\times10$$

= 480 $$cm^2$$