When comparing a square root with an integer, it's often easier to square both numbers and compare the results. This avoids having to estimate the square root. Also, recognizing common Pythagorean triples (like 3-4-5, 5-12-13, 8-15-17) can save time, although this problem doesn't use one.
The relationship cannot be determined from the information given.
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The Correct Option isB
Solution and Explanation
Step 1: Understanding the Concept:
The question asks us to find the length of the hypotenuse of a right triangle with given legs and compare it to a given value. Step 2: Key Formula or Approach:
We will use the Pythagorean theorem for a right triangle, which states that \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse. Step 3: Detailed Explanation:
From the image, we have a right triangle with:
Leg 1 (\(a\)) = 7
Leg 2 (\(b\)) = 8
Hypotenuse (\(c\)) = \(x\)
Applying the Pythagorean theorem:
\[ 7^2 + 8^2 = x^2 \]
\[ 49 + 64 = x^2 \]
\[ 113 = x^2 \]
\[ x = \sqrt{113} \]
Now we must compare the quantity in Column A (\(\sqrt{113}\)) with the quantity in Column B (15).
To compare \(\sqrt{113}\) and 15, we can compare their squares.
Square of Column A: \((\sqrt{113})^2 = 113\).
Square of Column B: \(15^2 = 225\). Step 4: Final Answer:
Since \(113<225\), it follows that \(\sqrt{113}<15\). Therefore, the quantity in Column B is greater.
