Question

Length of legs of a right-angled triangle are 7 cm and 24 cm. Find the length of altitude to the hypotenuse

Answer 1

By pythagoras  theorem a² + b² = c²

a and b are the legs whereas c is the hypotenuse

7² + 24² = c²

√( 49 + 576) = c

√ 625 = c

25 =c

Area of a right triangle is =  1/2 × product of legs of the right triangle

Area = 1/2 × 7 ×24

         = 84 cm²

Area of a triangle is  = 1/2 ×b×h

b = 25(hypotenuse) , h = ?(Let us say it is 'x' )

84 cm² = 1/2 × 25 ×  x

168 / 25 = x

6.72 = x

ANS = The altitude is 6.72 cm