Question

in ∆ABC, angle B= 90°. D is the midpoint of hypotenuse AC. If BD=4.5,then find the length of hypotenuse AC​

Answer 1

Given : In ∆ABC, ∠B = 90° , D is the midpoint of hypotenuse AC. BD = 4.5 cm

To find : find the length of hypotenuse AC.

solution : concept : in right angled triangle, the line joining the midpoint of hypotenuse to the right angled vertex is half of length of hypotenuse.

i.e., length of hypotenuse = 2 × length of the line from right angled angled vertex to midpoint of hypotenuse.

here for ∆ABC,

AC = 2 × BD = 2 × 4.5 cm = 9 cm

Therefore the length of hypotenuse AC = 9 cm