# The area of a right-angled triangle is 14 cm2, and one leg is 3 cm larger than the other. Find the legs.

August 31, 2021 | education

| Let’s say that one of the legs of this triangle is x cm.

The second leg is 3 cm larger, which means it is equal to x + 3 cm.

It is known that the area of a right-angled triangle is half the product of its legs, which means we get the following equation:

x * (x + 3) / 2 = 14,

x² + 3 * x = 28,

x² + 3 * x – 28 = 0.

The discriminant of this equation is:

D = 3² – 4 * 1 * (-28) = 9 + 112 = 121.

Since x can only be a positive number, the equation has a unique solution:

x = (- 3 + 11) / 2 = 4 (cm) – the length of one leg.

4 + 3 = 7 (cm) – the length of the second leg.

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