The hypotenuse of a rectangular tube is 10 cm, and one of its legs is 2 cm larger than the other.

The hypotenuse of a rectangular tube is 10 cm, and one of its legs is 2 cm larger than the other. Find the legs of the triangle.

Let us denote by a the length of that of the legs of a given right-angled triangle, which is the smallest.

In the wording of the condition for this task, it is reported that one of the legs of this right-angled triangle is 2 cm shorter than the other, therefore, the length of the larger leg should be equal to + 2 cm.

Since the hypotenuse of this right-angled triangle is 10 cm, using the Pythagorean theorem, we can compose the following equation:

c ^ 2 + (c + 2) ^ 2 = 10 ^ 2,

solving which, we get:

c ^ 2 + c ^ 2 + 4c + 4 = 100;

2c ^ 2 + 4c + 4 – 100 = 0;

2c ^ 2 + 4c – 96 = 0;

c ^ 2 + 2c – 48 = 0;

c = -1 ± √ (1 + 48) = -1 ± √49 = -1 ± 7;

c1 = -1 + 7 = 6;

c2 = -1 – 7 = -8.

Since the leg length cannot be negative, the value c = -8 is not suitable.

We find the 2nd leg:

c + 2 = 6 + 2 = 8.

Answer: 6 cm and 8 cm.