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

Question 540486: The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13cm, find the other two side.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let base be x
height = x-7
hypotenuse = 13
By Pythagoras theorem
leg1^2+leg2^2=13^2
x^2+(x-7)^2=169
x^2+x^2-14x+49=169
2x^2-14x-120=0
/2
x^2-7x-60=0
x^2-12x+5x-60=0
x(x-12)+5(x-12)=0
(x-12)(x+5)=0
Take the positive root
One leg =12
Other = 12-7=5
The sides are 5,12 & 13
m.ananth@hotmail.ca
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