Question

The altitude of right triangle is 7 cm less than its base if the hypotenues is 13 cm find other tw

Answer 1

let us consider a right triangle ABC.

let it base be x. so, it's altitude=x-7.

and given, hypotenuse=13cm.

now by applying pythagoras theorem

AC^2=AB^2+BC^2

(13)^2=(x-7)^2+x^2

169=x^2+x^2++49-14x

2x^2-14x+49-169=0

2x^2-14x-120=0

x^2-7x-60=0

x^2+12x-5x-60=0

x (x+12)-5 (x+12)

(x+12)(x-5)

either x=-12 (not possible )or, x=5

hence, base=5 cm altitude=14cm.