Suppose that the two television monitor has the same height. One has a conventional screen, which is 5in wider than it is high. The other has wider, which is 1.8 times as wide as it is high. The diagonal measure of the wider screen is 14in more than the diagonal measure of the smaller. What is the height of the screens?
If we let TV1 be the smaller and TV2 has the wider screen, then
Given on TV1Given on TV2w1=5+hw2=(1.8)hd1d2=14+d1
By Pythagorean Theorem,
d21=(5+h)2+h2d21=25+10h+h2+h2d21=25+10h+2h2d1=√2h2+10h+25(14+d1)2=(1.8h)2+h2196+28d1+d21=3.24h2+h2196+28d1+d21=4.24h2Equation 1
Substitute d1 and d21 in Equation 1
196+28√2h2+10h+25+2510h+2h2=4.24h2Combine like terms28√2h2+10h+25=2.24h2−10h−221Square both sides784(2h2+10h+25)=5.0176h4−44.8h3−990.08h2+4520h+488411568h2+7840h+19600=5.0176h4−44.8h3−990.08h2+4520h+488415.0176h4−44.8h3−2558.08h2−3320h+29241=0
Based from the graph the height that crosses the x-axis is at h≈27.90in
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