Find the area of a rectangle if its diagonal is 13 and one of the sides is 5.

1. Vertices of the rectangle – A, B, C, D. S – area of the rectangle. Diagonal AC = 13 units. CD = 5 units.

2. Calculate the side AD of the rectangle using the Pythagorean theorem:

AD = √AC² – СD² = √13² – 5² = √169 – 25 = √144 = 12 units.

3.Calculate the area of a rectangle equal to the product of the lengths of its sides AD and CD:

S = AD x CD = 12 x 5 = 60 units.

Answer: S = 60 units.