The hypotenuse of an isosceles triangle is 12√2. find the leg find the area.

An isosceles triangle is a triangle whose two sides are equal. These sides are called sides. If an isosceles triangle is right-angled, then its legs are lateral sides and, accordingly, are equal. Knowing the hypotenuse of a triangle, we find the legs according to the Pythagorean theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs, a² + b² = c².

Since the legs are equal, a = b, we have a² + a² = c².

2а² = с²;

a² = c² / 2;

a² = (12√2) ² / 2 = (144 * 2) / 2 = 144;

a = √144 = 12.

Find the area of ​​the triangle. The area of ​​a right-angled triangle is half the product of its legs. S = av / 2.

Since a = b, then S = a² / 2.

S = 12² / 2 = 144/2 = 72.

Answer. The leg is 12. The area is 72.