1995 AJHSME Problems/Problem 18

Problem

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

$[asy] draw((2,2)--(2,-2)--(-2,-2)--(-2,2)--cycle); draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle); draw((0,1)--(0,2)); draw((1,0)--(2,0)); draw((0,-1)--(0,-2)); draw((-1,0)--(-2,0)); [/asy]$

$\text{(A)}\ 25 \qquad \text{(B)}\ 44 \qquad \text{(C)}\ 50 \qquad \text{(D)}\ 62 \qquad \text{(E)}\ 75$

Solution

The area taken up by the L's is $4*\frac{3}{16}=\frac{3}{4}$ of the area of the whole square. What remains has $\frac{1}{4}$ of the area of the larger square. $\frac{100*100}{4}=\frac{100}{2}*\frac{100}{2}=50*50$ is the area of the smaller square, so its side length is 50. $\text{(C)}$

See Also

 1995 AJHSME (Problems • Answer Key • Resources) Preceded byProblem 17 Followed byProblem 19 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions