Find the length of the smaller leg of the triangle if you know that one of them is 7 cm less than the other, and the hypotenuse is 13 cm.

univerkov | December 18, 2020 | education

Let one leg be x, then the other is x-7. By the Pythagorean theorem: x ^ 2 + (x-7) ^ 2 = 13 ^ 2
x ^ 2 + x ^ 2 – 14x + 49 = 169
2x ^ 2 -14x -120 = 0 |: 2
x ^ 2 -7x -60 = 0
D = 49 + 240 = 289
x1 = (7 + 17) / 2 = 12
x2 = (7-17) / 2 = -5 – not suitable, because negative
Leg1 = 12, leg2 = 12-7 = 5
Answer: 5

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