The hypotenuse of a right triangle ahs a length of 13 cm. The sum of the lengths of the other two sides is 17 cm. Find the uknown side lengths.
I just happen to know that the answer is 5 and 12 but I will do the maths for you
1) x+ y = 17
2) x^2 + y^2 = 13^2= 169
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3) square 1)
(x+y)^2= 17^2 so x^2 +y^2 +2xy=289
4) take 2 from 3)
x^2+y^2+2xy -x^2-y^2=289-169
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so 2xy=120
xy=60
put x=60/y in 1
y + 60/y=17
multiply by y
y^2 + 60 = 17y
y^2-17y+60=0
or (y-5)(y-12)=0
so y=5 or 12
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