MathDB

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^\circ

angle, and the straight sides of the mountains form

45^\circ

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^{\circ}

",(.75,0),NE,fontsize(10pt)); label("

45^{\circ}

",(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]

<span class='latex-bold'>(A)</span>~4 \qquad <span class='latex-bold'>(B)</span>~5 \qquad <span class='latex-bold'>(C)</span>~4 \sqrt{2} \qquad <span class='latex-bold'>(D)</span>~6 \qquad <span class='latex-bold'>(E)</span>~5 \sqrt{2}

Credits to Countmath1 for the diagram.

Problem Statement