A rectangle is inscribed in an isosceles right triangle in such a way that it has a common

A rectangle is inscribed in an isosceles right triangle in such a way that it has a common right angle with the triangle. the perimeter of this rectangle is 25 cm. Find the leg of the triangle.

The ABC triangle is isosceles and rectangular, then the angle BAC = BCA = 45.

Since ВMНK is a rectangle, then ВM is parallel to KВ, ВK is parallel to MН.

Then, the angle AKН = ABC = 90, as the corresponding angles at the intersection of parallel KН and BC secant AB.

Then in the triangle AKН, AK = AН.

AK = KН, ВK = НM, then AK + ВK = KН + MН.

KН + MН = Pvmnk / 2 = 25/2 = 12.5 cm.

AB = BC = 12.5 cm.

Answer: The length of the leg of the triangle ABC is 12.5 cm.