Let's call one leg of the right triangle x cm. Then the other leg is (x+5) cm.
We can use the Pythagorean theorem to solve for x:
x^2 + (x+5)^2 = 25^2
x^2 + x^2 + 10x + 25 = 625
2x^2 + 10x - 600 = 0
Divide both sides of the equation by 2:
x^2 + 5x - 300 = 0
Factor the quadratic equation:
(x + 20)(x - 15) = 0
Thus, the possible solutions are x = -20 or x = 15.
Since the length of a leg can't be negative, x = 15 cm.
So one leg of the triangle is 15 cm and the other leg is 15 cm + 5 cm = 20 cm. Answer: \boxed{15 \text{ cm}, 20 \text{ cm}}.
One leg of a right triangle is 5 cm longer than the other leg. The hypotenuse is 25 cm long. Determine the measures of the legs of the triangle.
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