One of the sides of the rectangle is 12 cm, and its diagonal is 15 cm. The other side of the rectangle

One of the sides of the rectangle is 12 cm, and its diagonal is 15 cm. The other side of the rectangle is increased by 6 cm. What is the diagonal of the resulting rectangle?

First, let’s find the length of the second side of this rectangle. To do this, consider the triangle ΔABS and apply the Pythagorean theorem:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AB ^ 2 = AC ^ 2 – BC ^ 2;

AB ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81;

AB = √81 = 9 cm.

Now let’s increase the AB side by 6 cm:

A1B1 = AB + 6;

A1B1 = 9 + 6 = 15 cm.

Find the length of the diagonal of the resulting rectangle.

For this, we also apply the Pythagorean theorem:

A1C1 ^ 2 = A1B1 ^ 2 + B1C1 ^ 2;

A1C1 ^ 2 = 15 ^ 2 + 12 ^ 2 = 225 + 144 = 369;

A1C1 = √369 ≈ 19.2 cm.

Answer: the length of the diagonal of the resulting rectangle is 19.2 cm.