Question

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

Answer 1

Hint- Use pythagoras theorem ${\left( {hypotenuse} \right)^2} = {\left( {base} \right)^2} + {\left( {altitude} \right)^2}$ to find base and then use formula of area of right angled triangle $\dfrac{1}{2} \times base \times altitude$

Complete step-by-step answer:
Given,hypotenuse $ = 50$ cm and altitude $ = 40$ cm. We know that by pythagoras theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.The formula is written as-
 ${\left( {hypotenuse} \right)^2} = {\left( {base} \right)^2} + {\left( {altitude} \right)^2}$
$ \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}$ =$2500 - 1600 = 900$
So base$ = \sqrt {900} = 30$ cm
Now,Area of right angled triangle=$\dfrac{1}{2} \times base \times altitude$ $ \Rightarrow \dfrac{1}{2} \times 30 \times 40 = 30 \times 20 = 600$ ${cm}^{2}$
The area of the right angled triangle is 600 ${cm}^{2}$

Note: We use pythagoras theorem only for a right angled triangle. Most student will get confused because they know the formula as ${\left( {hypotenuse} \right)^2} = {\left( {base} \right)^2} + {\left( {altitude} \right)^2}$, but don’t get confused because altitude is perpendicular.