The length of the diagonal of a rectangle is 26 cm and one side is 10 cm. The area of the rectangle is:

The length of the diagonal of a rectangle is 26 cm and one side is 10 cm.

$$26^2\ =\ \left(length\ of\ another\ side\right)^2\ +10^2$$  [According to the pythagoras theorem.]

$$676\ =\ \left(length\ of\ another\ side\right)^2\ +100$$

$$676-100\ =\ \left(length\ of\ another\ side\right)^2\ $$

$$576\ =\ \left(length\ of\ another\ side\right)^2\ $$
$$24^2=\ \left(length\ of\ another\ side\right)^2\ $$
length of another side = 24 cm

Area of the rectangle = Product of both side

= $$24\times10$$

= 240 $$cm^2$$