Question

In a right angled triangle the hypotenuse is 10 cm more than the shortest side.If third side is 6 cm less than hypotenuse,find the sides of triangle

Answer 1

Answer:

In a right angled triangle the hypotenuse is 10 cm more than the shortest side.If third side is 6 cm less than hypotenuse then

Shorter side = 16.95 cm

Third side = 20.95 cm

Hypotenuse = 26.95 cm

Step-by-step explanation:

Let say shorter side = s

Hypotenuse = s + 10

Third side = s+10-6 = s + 4

using Pythagoras theorem

(s +10)² = s² + (s+4)²

=> s² + 100 + 20s = s² + s² + 16 + 8s

=> s² - 12s - 84 = 0

=> s = (12 ± √(12² - 4(1)(-84)) )/2

= (12 ± √(144 + 4*84) )/2

= 6 ± √(36 + 84)

= 6 ± √120

= 6 ± 10.95

= 16.95 cm  ( as length can not be -ve)

Shorter side = 16.95 cm

Third side = 20.95 cm

Hypotenuse = 26.95 cm