Question

Find the area of a right triangle with hypotenuse $50cm$ and altitude $40cm$.

Answer 1

Area of a right angled triangle$=\frac{1}{2}\times$base$\times$altitude

Given:hypotenuse$=50$cm and altitude$=40$cm

By Pythagoras theorem, ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(altitude\right)}^2$

$\Rightarrow {\left(50\right)}^2={\left(base\right)}^2+{\left(40\right)}^2$

$\Rightarrow {\left(base\right)}^2={\left(50\right)}^2-{\left(40\right)}^2=2500-1600=900$

$\Rightarrow$ base$=\sqrt{900}=30$cm

$\therefore$ base$=30$cm

$\therefore$Area of a right angled triangle$=\frac{1}{2}\times$base$\times$altitude

$=\frac{1}{2}\times 30\times 40=30\times 20=600$sq.cm