In a right-angled triangle, one leg is 3 cm larger than the other. The area of the triangle is 9 cm2. What is the larger leg?

Let’s apply the area formula for a right-angled triangle, that is, the area of ​​a right-angled triangle is half the product of the legs. Or, if we denote by a and b – legs, then: S = 1/2 * a * b. In this case, let the leg a be equal to x (cm), and the leg b is larger than leg a by 3 (cm) or (x + 3) (cm).

Substitute the values ​​into the area formula:

9 = 1/2 * x * (x + 3).

9 = 1/2 * x ^ 2 + 3/2 * x.

9 * 2 = 1 * 2 * x ^ 2/2 + 3 * 2 * x / 2.

18 = x ^ 2 + 3 * x.

x ^ 2 + 3 * x – 18 = 0.

D = 32 – 4 * 1 * (-18) = 9 + 72 = 81.

x1 = (-3 + √81) / (2 * 1) = (-3 + 9) / 2 = 6/2 = 3.

We do not take a negative value into account.

Therefore, the smaller leg is 3 centimeters, then 3 (cm) + 3 (cm) = 6 (cm) is the length of the larger leg.

Answer: 6 centimeters is the length of the larger leg.