Question

in a right angled triangle the perimeter of a rectangle is 60m and its hypotenuse is 25m find other two sides

Answer 1

let the triangle be ABC right angled at B.
perimeter= 60 cm (given)
so, AB+ BC + AC= 60 cm
and AC= 25 cm
Also, AB+ BC = 60- 25= 35 cm
AB= 35-BC
AB²= (35-BC)²___________(1)
AND using PGT in ABC
H²=B²+P²
25²=B²+P²
625= B²+P²
625= BC²+AB²
AB²=625-BC²____________(2)
By (1) and (2),we get
625-BC²=(35-BC)²
625-BC²=1225+BC²-70BC
2BC²-70BC+600=0
BC²-35BC+300=0(on dividing both sides by 0)
we get an quadratic equation as :-
BC²-35BC+300=0
BC²-20BC-15BC+300=0
BC(BC-20)+15(BC-20)=0
(BC-20)(BC+15)=0
BC=20 or BC= -15
BC= -15 ( not taken because side of a triangle cant be negative)
so we take BC= 20 cm
Also AB+ BC= 35
so , AB= 35-BC
       AB= 35-20
      AB = 15 cm
so other sides of triangle are AB=15cm , BC= 20 cm , AC= 25
that can satisfy that  their perimeter = 15+ 20 + 25= 60 cm