The hypotenuse of a right-angled triangle is 51 cm, legs are in relation to 8:15. Find the smaller leg.

In a right-angled triangle, you can find the unknown side according to the Pythagorean theorem, which says: the sum of the squares of the legs is equal to the square of the hypotenuse. Let’s solve the problem using the equation, where:
8x – the smaller leg of the triangle;
15x – larger leg of the triangle;
Then the hypotenuse is equal to:
8x² + 15x² = 51²;
23x² = 51²;
23x² = 2601;
х² = 2601/23;
x² = 113 2/23 (113 integer 2/23);
x = √113 2/23;
8x = 8 * √113 2/23 = √7237 13/23 = 85 √12 13/23 cm – smaller leg of a right triangle