Find the diagonal of a rectangle if its perimeter is 62, and the perimeter

Find the diagonal of a rectangle if its perimeter is 62, and the perimeter of one of the triangles into which the diagonal divided the triangle is 56

Let us denote the lengths of the sides of this rectangle by a and b, and the length of the diagonal of this rectangle by d.

According to the condition of the problem, the perimeter of this rectangle is 62, therefore, we can write the following relation:

2 * (a + b) = 62.

We find from the obtained ratio the sum of the lengths of the sides of this rectangle:

a + b = 62/2;

a + b = 31.

By the statement of the problem, the perimeter of one of the triangles into which the diagonal divided the triangle is 56.

Since the sides of this triangle are two sides of the rectangle and the diagonal of the rectangle, we can write the following relationship:

a + b + d = 56.

Knowing the sum of the lengths of the sides of a given rectangle, we find the diagonal:

d = 56 – a – b = 56 – (a + b) = 56 – 31 = 25.

Answer: The diagonal of the rectangle is 25.