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