A right-angled triangle has two equal legs and its hypotenuse measures 10 cm. What is the area of the triangle?

In a 45°–45°–90° triangle the hypotenuse is √2 times a leg, so each leg is 10/√2 = 5√2 cm. The two legs enclose the right angle, so the area = ½ × 5√$2\times 5$√2 = ½ $\times 50=25{\text{cm}}^2$. Using 10 as a leg instead of the hypotenuse would wrongly give $50{\text{cm}}^2$.