Question

The area of each of the four congruent L-shaped regions of this $100$ -inch by $100$ -inch square is $\dfrac{3}{16}$ of the total area. How many inches long is the side of the center square?

$25$

$44$

$50$

$62$

$75$

Solution:

The four L-shaped regions cover $4 \times \dfrac{3}{16} = \dfrac34$ of the square, so the center square is the remaining $\dfrac14$ of the total area.

The total area is $100 \times 100 = 10000$ square inches, so the center square has area $\dfrac14 \times 10000 = 2500,$ and its side is $\sqrt{2500} = 50$ inches.

Thus, the correct answer is C .

1995 AMC 8 Problem 18

Solution:

Problem 18 in Other Years