Question

ABCD is a square of 20 m. What is the area of the least-sized square that can be inscribed in it with its vertices on the sides of ABCD?

• A. \( 100 \, \text{m}^2 \)
• B. \( 120 \, \text{m}^2 \)
• C. \( 200 \, \text{m}^2 \)
• D. \( 250 \, \text{m}^2 \)

Hint:

When solving for the area of an inscribed square, remember that the relationship between the side length of the outer square and the area of the inscribed square involves squaring the side length and then halving the result.

Answer 1

The Correct Option is C

To find the area of the least-sized square that can be inscribed in a larger square (with its vertices touching the sides of the square), we use the formula: \[ \text{Area of inscribed square} = \frac{1}{2} \times \text{side length of outer square}^2 \] Substituting the given value: \[ \text{Area} = \frac{1}{2} \times 20^2 = \frac{1}{2} \times 400 = 200 \, \text{m}^2 \] Final Answer: The correct answer is (c) \( 200 \, \text{m}^2 \).