Question:
If the area of a square is 64 cm², what is the length of its diagonal?
If the area of a square is 64 cm², what is the length of its diagonal?
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For a square's diagonal, use $d = s\sqrt{2}$, where $s$ is the side length derived from the area.
Updated On: Jul 28, 2025
- 8 cm
- $8\sqrt{2}$ cm
- 16 cm
- $16\sqrt{2}$ cm
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The Correct Option is B
Solution and Explanation
- Step 1: Area of square = $s^2 = 64$, so side $s = \sqrt{64} = 8$ cm.
- Step 2: Diagonal of a square = $s\sqrt{2} = 8\sqrt{2}$ cm.
- Step 3: Verify using Pythagoras: Diagonal = $\sqrt{s^2 + s^2} = \sqrt{64 + 64} = \sqrt{128} = 8\sqrt{2}$.
- Step 4: Check options: Option (b) is $8\sqrt{2}$ cm, which matches.
- Step 5: Ensure no miscalculation in area or formula.
- Step 6: Option (b) is correct.
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