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= Skip to navigation
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GPT-4o mini
Let's solve the equation step by step.
1. Start with the given equation:
\[ a^2 + 162 = 202 \]
2. Subtract 162 from both sides to isolate \( a^2 \):
\[ a^2 = 202 - 162 \]
\[ a^2 = 40 \]
3. Take the square root of both sides to solve for \( a \):
\[ a = \sqrt{40} \]
4. Simplifying \( \sqrt{40} \):
\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Thus, the missing side length is:
\[ a = 2\sqrt{10} \]
If you need a numerical approximation, \( \sqrt{10} \approx 3.162 \), so:
\[ a \approx 2 \times 3.162 \approx 6.324 \]
However, if you are looking for an exact numerical answer to enter, you should enter:
\[ 2\sqrt{10} \]
or its approximate value:
\[ 6.324 \]
(Note: Please clarify if you need the exact form or the numerical approximation.)
1. Start with the given equation:
\[ a^2 + 162 = 202 \]
2. Subtract 162 from both sides to isolate \( a^2 \):
\[ a^2 = 202 - 162 \]
\[ a^2 = 40 \]
3. Take the square root of both sides to solve for \( a \):
\[ a = \sqrt{40} \]
4. Simplifying \( \sqrt{40} \):
\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Thus, the missing side length is:
\[ a = 2\sqrt{10} \]
If you need a numerical approximation, \( \sqrt{10} \approx 3.162 \), so:
\[ a \approx 2 \times 3.162 \approx 6.324 \]
However, if you are looking for an exact numerical answer to enter, you should enter:
\[ 2\sqrt{10} \]
or its approximate value:
\[ 6.324 \]
(Note: Please clarify if you need the exact form or the numerical approximation.)
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