Question

if the perimeter of a right angled triangle is 30 cm and its hypotenuse is 13 cm what is the measure of the other two sides?

Answer 1

Let the sides be x,y

Perimeter =13+x+y

x+y+13=30

x+y=17...(1)

We know :

x^2+y^2=13^2[By pythagoras theorem]

x^2+y^2=169...(2)

(x+y)^2=17^2[see(1)]

x^2+y^2+2xy=289[see(2)]

2xy=289-169

=xy=120/2=60...(3)

x=17-y[see (1)]

y*(17-y)=60

y^2-17y+60=0

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

y(y-12)-5(y-12)=0

Either y=12 or 5

For either values both the sides will be 12 and 5

So measure of 2 other sides =12 and 5cm