Question

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

Answer 1

let base be`x`cm
altitude`= (x-7)`cm
hypotenuse`= 13`cm
acc to pythagoras theorem
`x^2 + (x-7)^2 = 13^2`
`x^2 + x^2 - 14x + 49 = 169`
`2x^2 - 14x - 120=0`
`x^2 - 7x - 60=0`
`x^2 - 12x + 5x - 60=0`
`x(x-12)+5(x-12)=0`
`(x-12)(x+5)=0`
`x-12=0 or x+5=0`
`x=12,-5`
base cant be negative so `x=12` answer