The difference between the legs in a right-angled triangle is 1 cm, and the hypotenuse is 29 cm.

| August 10, 2021 | education

The difference between the legs in a right-angled triangle is 1 cm, and the hypotenuse is 29 cm. Find the perimeter of this triangle.

Let the length of the leg BC = X cm, then, by condition, the length of the leg AC = (X + 1) cm.

In a right-angled triangle ABC, according to the Pythagorean theorem:

AB ^ 2 = AC ^ 2 + BC ^ 2.

841 = (X + 1) ^ 2 + X ^ 2 = X ^ 2 + 2 * X + 1 + X ^ 2.

2 * X ^ 2 + 2 * X – 840 = 0.

X ^ 2 + X = 420 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 12 – 4 * 1 / (-420) = 1 + 1680 = 1681.

X1 = (-1 – √1681) / (2 * 1) = (-1 – 41) / 2 = -42 / 2 = -21. (Doesn’t fit because <0).

X2 = (-1 + √1681) / (2 * 1) = (-1 + 41) / 2 = 40/2 = 20.

BC = 20 cm, then AC = 20 + 1 = 21 cm.

Ravs = 29 + 20 + 21 = 70 cm.

Answer: The perimeter of the triangle is 70 cm.



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