In an isosceles right-angled triangle with 13 cm legs, a rectangle is inscribed

In an isosceles right-angled triangle with 13 cm legs, a rectangle is inscribed, which has a greater angle with the triangles. Find the perimeter of the rectangle.

Since KСНМ is a rectangle, then СK = МН, КМ = СН.

Let the length of the segment CH = KM = X cm, then BH = (13 – X) cm.

Consider the BNM triangle. Angle MBH = 45, angle НМВ = CAD = 45 as the corresponding angles at the intersection of parallel straight lines АС and МН secant AB. Then the triangle BNM is rectangular and isosceles, HM = CK = BH = (13 – X) cm.

Then the perimeter of KCHM will be equal to: P = 2 * (X + (13 – X) = 2 * X + 26 – 2 * X = 26 cm.

Answer: The perimeter of the rectangle is 26 cm.