The sum of the legs of a right-angled triangle is 79 cm. If one of the legs is increased by 23 cm and the other

The sum of the legs of a right-angled triangle is 79 cm. If one of the legs is increased by 23 cm and the other reduced by 11 cm, then the new right-angled triangle will have a hypotenuse of the same length as this one. find the lengths of the legs of this triangle.

1. For a right-angled triangle, the sum of the legs is known: Sk;

Sk = X + Y = 79 cm;

Y = 79 – X;

2. The hypotenuse of the triangle is: Z = X² + Y²;

3. We increase the first leg:

X1 = X + 23;

4. Reduce the second leg:

Y1 = Y – 11;

5. Hypotenuse of the new triangle: Z1 = X1² + Y1²;

6. According to the problem statement: Z1 = Z;

X1² + Y1² = X² + Y²;

(X + 23) + (Y – 11) = X² + Y²;

7. Substitute:

(X + 23) ² + (79 – X – 11) ² = X² + (79 – X) ²;

X² + 46 * X + 529 + 4624 – 136 * X + X² = X² + 6241 – 158 * X + X²;

68 * X = 1088;

X = 1088/68 = 16 cm;

Y = 79 – 16 = 63 cm.

Answer: the length of the first leg is 16 cm, the second is 63 cm.