Find the diagonal of the rectangle if one side of the rectangle is 9 cm and the other is 3 cm larger?

Given: ABCD is a rectangle,

AB = 9 cm, BC =? 3 cm> AB.

Find: AC =? cm

Solution:

1) BC = 9 + 3 = 12 cm.

2) the diagonal AC forms with the sides of the rectangle AB and BC a right-angled triangle ABC, in which AB and BC are the legs, AC is the hypotenuse.

By the theorem, the square of the hypotenuse is equal to the sum of the squares of the legs: AC ^ 2 = AB ^ 2 + BC ^ 2.

Substitute the data: AC ^ 2 = 9 ^ 2 + 12 ^ 2,

AC ^ 2 = 81 + 144 = 225,

AC = root of 225 = 25 cm.

Answer: AC = 25 cm.