Question

202+x2=292
Using the information given above, find AE. Round to the nearest tenth if necessary.(2 points)
AE =

Answer 1

To solve for AE, we first need to simplify the given equation:

\[
202 + x^2 = 292
\]

Subtract 202 from both sides:

\[
x^2 = 292 - 202
\]
\[
x^2 = 90
\]

Now take the square root of both sides to solve for \(x\):

\[
x = \sqrt{90}
\]

The square root of 90 can be simplified further:

\[
\sqrt{90} = \sqrt{9 \times 10} = 3\sqrt{10}
\]

Now, we can calculate \(3\sqrt{10}\):

Using \( \sqrt{10} \approx 3.162 \):

\[
x \approx 3 \times 3.162 \approx 9.486
\]

Rounding to the nearest tenth:

\[
x \approx 9.5
\]

If AE corresponds to the value of \(x\) from the equation, then:

\[
AE \approx 9.5
\]

Thus,

\[
\text{AE} \approx 9.5
\]