MathDB
Inscribed square

Source: 2015 AMC8 #25

November 25, 2015
AMCAMC 8geometry

Problem Statement

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?
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>1212<spanclass=latexbold>(C)</span>15<spanclass=latexbold>(D)</span>1512<spanclass=latexbold>(E)</span>17 <span class='latex-bold'>(A) </span> 9\qquad <span class='latex-bold'>(B) </span> 12\frac{1}{2}\qquad <span class='latex-bold'>(C) </span> 15\qquad <span class='latex-bold'>(D) </span> 15\frac{1}{2}\qquad <span class='latex-bold'>(E) </span> 17
[asy] 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]