Question 378256
  <pre><font size = 3 color = "indigo"><b>
Hi,
lengths of the legs have a sum of 17 centimeters
Let x and (17-x) represent the lengths of the legs
hypotnuse of this right triqangle measures 13 centimeters
Applying the Pythagorean Theorem
x^2 + (17-x)^2 = 13cm^2
solving for x
x^2 + 17^2 - 34x + x^2 = 13^2
2x^2 -34x +120 = 0
x^2 -17x + 60 = 0
factoring
(x-12)(x-5)= 0
(x-12)=0 x = 12
(x-5)= 0 x = 5
the lengths of the legs are 12cm and 5cm
CHECKING our Answer
144 + 25 = 169