Question

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm find the other 2 sides

Answer 1

let x be its base. then its altitude becomes x-7
by pythagoras theorem
x2+(x-7)2= (13)2
x2 + x2 -14x + 49 = 169
2x2 -14x =169-49= 120
2x2-14x=120
divide it by 2
x2-7x=60
x2-7x-60
x2-12x+5x-60
x (x-12)+5 (x-12)
(x+5) (x-12)
,', x=-5 or 12
hence x=base =12cm altitude or another side =x-7
=12-7=5cm

Answer 2

Let base be X cm then altitude become X-7******now by Pythagoras theorm 13^2=x^2 +(x-7)^2 **** . *********************** . . 169=X^2 +x^2 - 14x+49 ******* ** . . . *****2x^2+49-169+14x.............now2(X^2+7x-60)=0******x^2+5x-12x-60=0********x(x+5)-12(x+5). . . So. X=-5and.""x=12now neglected - 5so base=12 and height =12-7=5