Difference between revisions of "2015 AMC 8 Problems/Problem 25"
(Created page with "One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space? <math> ...") |
(→Video Solutions) |
||
| (111 intermediate revisions by 48 users not shown) | |||
| Line 1: | Line 1: | ||
| + | == Problem == | ||
| + | |||
| + | |||
One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space? | One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space? | ||
| − | |||
| − | |||
<asy> | <asy> | ||
| + | size(75); | ||
draw((0,0)--(0,5)--(5,5)--(5,0)--cycle); | draw((0,0)--(0,5)--(5,5)--(5,0)--cycle); | ||
filldraw((0,4)--(1,4)--(1,5)--(0,5)--cycle, gray); | filldraw((0,4)--(1,4)--(1,5)--(0,5)--cycle, gray); | ||
| Line 10: | Line 12: | ||
filldraw((4,4)--(4,5)--(5,5)--(5,4)--cycle, gray); | filldraw((4,4)--(4,5)--(5,5)--(5,4)--cycle, gray); | ||
</asy> | </asy> | ||
| + | |||
| + | <math>\textbf{(A) } 9\qquad \textbf{(B) } 12\frac{1}{2}\qquad \textbf{(C) } 15\qquad \textbf{(D) } 15\frac{1}{2}\qquad \textbf{(E) } 17</math> | ||
| + | |||
| + | |||
| + | ==Video Solutions== | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | https://youtu.be/rTljQV79PCY | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | https://youtu.be/51K3uCzntWs?t=3358 | ||
| + | |||
| + | ~ pi_is_3.14 | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | |||
| + | {{AMC8 box|year=2015|num-b=24|after=Last Problem}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 10:02, 23 July 2024
Problem
One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?
![[asy] size(75); draw((0,0)--(0,5)--(5,5)--(5,0)--cycle); filldraw((0,4)--(1,4)--(1,5)--(0,5)--cycle, gray); filldraw((0,0)--(1,0)--(1,1)--(0,1)--cycle, gray); filldraw((4,0)--(4,1)--(5,1)--(5,0)--cycle, gray); filldraw((4,4)--(4,5)--(5,5)--(5,4)--cycle, gray); [/asy]](http://latex.artofproblemsolving.com/1/6/9/16905c0611e83380a7ff4045538ffe74a49c7cb7.png)
Video Solutions
~savannahsolver
https://youtu.be/51K3uCzntWs?t=3358
~ pi_is_3.14
See Also
| 2015 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Last Problem | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
