Question

The hypotenuse of a right triangle is cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be cm. How long are the legs of the triangle?

Answer 1

smaller leg is 3cm and longer leg is 9 cm

The hypotenuse of a right triangle is 3√10 cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be 9√5 cm. How long are the legs of the triangle?

let smaller leg is x and longer leg is y.

from Pythagoras theorem,

x² + y² = (3√10)²

⇒x² + y² = 90 ........(1)

again, smaller leg is tripled and longer leg is doubled then new hypotenuse will be 9√5 cm

from Pythagoras theorem,

(3x)² + (2y)² = (9√5)²

⇒9x² + 4y² = 81 × 5 = 405 ........(2)

from equations (1) and (2) we get,

9x² + 4y² - 4(x² + y²) = 405 - 4 × 90

⇒9x² - 4x² = 405 - 360

⇒5x² = 45

⇒x = 3

and y = √(90 - x²) = √(90 - 9) = 9