Question

the altitude of a right triangle is 7 cm less than its base. if the hypotenuse is 13cm find the other two sides.

Answer 1

Let base = x cm : altitude = x - 7 cm Hypotenuse = 13 cm Using pythagoras theorem  x^2 + (x-7)^2 = 13^2 x^2 + x^2 +49 - 14x = 169 2x^2  - 14x = 120 2x^2 - 14x - 120 = 0 x^2 - 7x - 60 = 0 Now quadratic is formed.... x^2 -12x + 5x -60 = 0 x ( x -12) + 5 ( x - 12 ) = 0 (x-12 )(x+5) =0 x=12........x= -5 ( neglecting neg. Value) x=12  

Answer 2

Hi ,

Let the base of the triangle ( b ) = x cm

altitude of the triangle = a = ( x - 7 ) cm

Hypotenuse ( c ) = 13 cm

a² + b² = c²

[ By Phythogarian theorem ]

( x - 7 )² + x² = 13²

x² - 14x + 49 + x² - 169 = 0

2x² - 14x - 120 = 0

divide each term with 2 , we get

x² - 7x - 60 = 0

x² - 12x + 5x - 60 = 0

=> x( x - 12 ) + 5( x - 12 ) = 0

=> ( x - 12 )( x + 5 ) = 0

Therefore ,

x - 12 = 0 or x + 5 = 0

x = 12 or x = -5

x should not be negative .

x = 12

base = b = 12 cm

altitude = ( x - 7 ) = 12 - 7 = 5cm

I hope this helps you.

: )