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 

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