We are given a shape that is almost a rectangle, but with a slanted side. The lengths of three sides are given as 21 cm, 29 cm, and 15 cm. We are asked to find the length of the fourth side, labeled as $x$.

1. Problem Description

We are given a shape that is almost a rectangle, but with a slanted side. The lengths of three sides are given as 21 cm, 29 cm, and 15 cm. We are asked to find the length of the fourth side, labeled as $x$.

2. Solution Steps

First, let's complete the rectangle. Drop a vertical line from the endpoint of the 21 cm side to the 29 cm side. This creates a rectangle with sides 21 cm and 29 cm, and a right triangle.

The base of the right triangle is the difference between the sides of length 29 cm and 21 cm, which is $29 - 21 = 8$ cm.

The height of the right triangle is the difference between the sides of length 21 cm and 15 cm, which is $21 - 15 = 6$ cm.

The side $x$ is the hypotenuse of this right triangle.

We can use the Pythagorean theorem to find $x$. The Pythagorean theorem states:

$a^2 + b^2 = c^2$, where $a$ and $b$ are the legs of a right triangle and $c$ is the hypotenuse.

In this case, $a = 6$ and $b = 8$, and we want to find $c = x$.

So, $6^2 + 8^2 = x^2$.

$36 + 64 = x^2$

$100 = x^2$

Taking the square root of both sides:

$x = \sqrt{100} = 10$

3. Final Answer

$x = 10$