# One of the legs is 2 cm larger than the other, find the legs if the hypotenuse is 12 cm.

March 24, 2021 | education

| It is known from the condition that one of the legs is 2 cm larger than the other. And the length of the hypotenuse is also known 12 cm.

In order to find what the legs of a right-angled triangle are equal to, we will use the Pythagorean theorem.

But first of all, we introduce the variable x, denoting the din from the legs, then the second leg is (x + 2).

We apply the Pythagorean theorem and get the equation:

x ^ 2 + (x + 2) ^ 2 = 12 ^ 2;

x ^ 2 + x ^ 2 + 4x + 4 – 144 = 0;

2x ^ 2 + 4x – 140 = 0;

x ^ 2 + 2x – 70 = 0;

D = 284; √D = 2√71.

x1 = (-2 + 2√71) / 2 = √71 – 1;

x2 = (-2 – 2√71) / 2 = -1 – √71 does not fit.

One leg is equal to √71 – 1 cm, the second √71 + 1 cm.

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