Question

in a right angle triangle the hypotenuse is 10 cm more than the shortest side. if the third side is 6cm less than the hypotenuse, find the sides of the right angle triangle.

Answer 1

let short side be x:-

therefore, hypotenuse = (10+x)cm

and third side = (10+x)-6

= 10-6+x

= (4+x)cm

By using Pythagoras theorem :-

$( {h})^{2} = ( {b})^{2} + ( {p})^{2}$

$( {10 + x})^{2} = ( {4 + x})^{2} + {x}^{2}$

$100 + {x}^{2} + 20x = 16 + {x}^{2} + {8x} + {x}^{2}$

$100 - 16 = 8x - 20x + {x}^{2}$

$84 = - 16x + { x}^{2}$

$- {x}^{2} + 16x + 84 = 0$