Problems(1)
Jean made a piece of stained glass art in the shape of two mountains, as shown in the figure below. One mountain peak is 8 feet high and the other peak is 12 feet high. Each peak forms a 90∘ angle, and the straight sides of the mountains form 45∘ with the ground. The artwork has an area of 183 square feet. The sides of the mountains meet at an intersection point near the center of the artwork, h feet above the ground. What is the value of h?[asy]
unitsize(.3cm);
filldraw((0,0)--(8,8)--(11,5)--(18,12)--(30,0)--cycle,gray(0.7),linewidth(1));
draw((-1,0)--(-1,8),linewidth(.75));
draw((-1.4,0)--(-.6,0),linewidth(.75));
draw((-1.4,8)--(-.6,8),linewidth(.75));
label("8",(-1,4),W);
label("12",(31,6),E);
draw((-1,8)--(8,8),dashed);
draw((31,0)--(31,12),linewidth(.75));
draw((30.6,0)--(31.4,0),linewidth(.75));
draw((30.6,12)--(31.4,12),linewidth(.75));
draw((31,12)--(18,12),dashed);
label("45∘",(.75,0),NE,fontsize(10pt));
label("45∘",(29.25,0),NW,fontsize(10pt));
draw((8,8)--(7.5,7.5)--(8,7)--(8.5,7.5)--cycle);
draw((18,12)--(17.5,11.5)--(18,11)--(18.5,11.5)--cycle);
draw((11,5)--(11,0),dashed);
label("h",(11,2.5),E);
[/asy]<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 42<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 52Credits to Countmath1 for the diagram. AMC 82024 AMC 8