The hypotenuse of an isosceles right-angled triangle is 7√2. Find the leg.

Since, according to the condition of the problem, a right-angled triangle is isosceles, its legs are equal to each other. Let them be equal to x.

By the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Since the hypotenuse is 7√2, we compose an equation and find the length of the legs from it:

x² + x² = (7√2) ²;

2x² = 98;

x² = 49;

x = 7.

Using the Pythagorean theorem, we found the length of the leg, since the triangle is isosceles, then the second leg is 7.

Answer: 7.