The legs of a right triangle are 7 and 24. find the hypotenuse of a triangle like this one if one of the legs is 10.

By the Pythagorean theorem, the hypotenuse of the first triangle:

c² = a² + b², where a and b are legs, c is hypotenuse; a = 7; b = 24;

c² = 7² + 24² = 49 + 576 = 625; c = √625 = 25;

Triangle a’b’c ‘is similar to triangle abc.

Two cases are possible:

1) a ‘= 10;

Similarity coefficient: k = a / a ‘= 7/10; c ‘= 25: 7/10 = 250/7 = 35 5/7;

2) b ‘= 10;

k = b / b ‘= 24/10; c ‘= 25: 24/10 = 250/24 = 10 5/12.