Find the leg of a right-angled triangle if it is known that 1 of them is 4 cm larger than the other

Find the leg of a right-angled triangle if it is known that 1 of them is 4 cm larger than the other, and the area of the triangle = 30 cm2.

Let the length of the leg AC be equal to X cm, then the length of the leg AB, by condition, will be (X + 4) cm.

The area of a right-angled triangle is half the product of its legs.

Savs = AC * AB / 2.

30 = X * (X + 4) / 2.

X ^ 2 + 4 * X – 60 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 4 ^ 2 – 4 * 1 * (-60) = 16 + 240 = 256.

X1 = (-4 – √256) / (2 * 1) = (-4 – 16) / 2 = -20 / 2 = -10. (Doesn’t fit because <0).

X2 = (-4 + √256) / (2 * 1) = (-4 + 16) / 2 = 12/2 = 6.

AC = 6 cm.

AB = 6 + 4 = 10 cm.

Answer: The length of the legs is 6 cm and 10 cm.