We are given a composite figure. We need to find the length of side $x$ to the nearest tenth.

1. Problem Description

We are given a composite figure. We need to find the length of side $x$ to the nearest tenth.

2. Solution Steps

First, complete the rectangle by drawing a horizontal line from the top of the segment labeled 17 to the segment labeled

8. Also, complete the right triangle by drawing a vertical line from the vertex where $x$ begins, to the horizontal line segment just drawn.

Let's call the length of the new horizontal segment $a$, and the length of the new vertical segment $b$.

The length of $a$ is the horizontal distance, which is $5$.

$a = 5$

The length of $b$ is the vertical distance, which is $17 - 8 = 9$.

$b = 9$

Now we have a right triangle with legs of length $a=5$ and $b=9$. The hypotenuse is $x$. By the Pythagorean theorem,

$x^2 = a^2 + b^2$

$x^2 = 5^2 + 9^2$

$x^2 = 25 + 81$

$x^2 = 106$

$x = \sqrt{106}$

$x \approx 10.2956$

Rounding $x$ to the nearest tenth gives us $x \approx 10.3$.

3. Final Answer

1

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