In the rectangle, the diagonal is 25, and one of the sides is 15. Find the legs of an isosceles right triangle

In the rectangle, the diagonal is 25, and one of the sides is 15. Find the legs of an isosceles right triangle that is equal to it.

Since the triangle ABC is rectangular, we determine the length of the leg AD by the Pythagorean theorem.

AD ^ 2 = BD ^ 2 – AB ^ 2 = 625 – 225 = 400.

АD ^ 2 = 20 cm.

Let’s define the area of the rectangle ABCD.

Savsd = AB * AD = 15 * 20 = 300 cm2.

Let’s define the legs of an isosceles triangle with an area of 300 cm2.

Let the legs of the triangle be equal to X cm.

Then X ^ 2/2 = 300 cm2.

X ^ 2 = 600.

X = √600 = 10 * √6 cm.

Answer: The legs of the triangle are 10 * √6 cm.