# The sum of the lengths of the legs of a right-angled triangle is 34 cm, and the length of the hypotenuse

The sum of the lengths of the legs of a right-angled triangle is 34 cm, and the length of the hypotenuse is 26 cm. Find the lengths of the legs

Let x cm be the length of the first leg, then (34-x) cm is the length of the second leg.
According to the Pythagorean theorem: the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
x ^ 2 + (34-x) ^ 2 = 26 ^ 2
x ^ 2 + 34 ^ 2-2 * 34 * x + x ^ 2 = 26 ^ 2
x ^ 2 + 1156-68x + x ^ 2-676 = 0
2 * x ^ 2-68x + 480 = 0
x ^ 2-34x + 240 = 0
D = (- 34) ^ 2-4 * 240 = 1156-960 = 196
root D = 14
x1 = (34-14) / 2 = 20/2 = 10
x2 = (34 + 14) / 2 = 48/2 = 24
We got that 10cm is the length of one of the legs, 34-10 = 24cm is the length of the second leg.
Answer: 10 cm and 24 cm.

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