Difference between revisions of "1995 AJHSME Problems/Problem 18"

(Problem)
Line 4: Line 4:
  
 
<asy>
 
<asy>
draw((2,2)--(2,-2)--(-2,-2)--(-2,2)--cycle);
+
draw((20,2)--(2,-2)--(-2,-2)--(-2,2)--cycle);
 
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
 
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
 
draw((0,1)--(0,2));
 
draw((0,1)--(0,2));

Revision as of 14:03, 19 October 2016

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((20,2)--(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 (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 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