Question

Use the equation to find the length of the missing leg measure.



NOTE: Type in numerical answers only to receive credit.

(3 points)
a2+162=202

1. Evaluate the powers: a2+ =400

2. Isolate the variable: a2=

3. Take the square root of both sides: a2−−√=144−−−√

4. The missing side length is a=

Answer 1

Let's solve the equation step by step.

Given the equation:

\[ a^2 + 162 = 202 \]

1. **Evaluate the powers**:
Since \( a^2 + 162 = 202 \), we want to simplify this first.
Subtract 162 from both sides:
\[ a^2 + 162 - 162 = 202 - 162 \]
\[ a^2 = 40 \]

2. **Isolate the variable**:
From step 1, we have already isolated \( a^2 \):
\[ a^2 = 40 \]

3. **Take the square root of both sides**:
\[ a = \sqrt{40} \]

4. **Calculate the square root**:
The square root of 40 can be simplified:
\[ a = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \]
For numerical approximation, \( \sqrt{40} \approx 6.32 \) (if needed), but keep in mind to use the exact value for the final answer.

So, the final answer is:
The missing side length is \( a = \sqrt{40} \) which approximately equals 6.32.
If you need numerical answers only, you can provide \( 6.32 \) (or the exact value \( 6.32455532 \) if more precision is required).

For full completion, using the exact square root of the simplified form:
The missing side length is \( a \approx 6.32 \) or \( 2\sqrt{10} \).