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Pls solve fast

Q.7. For going to a city B from city A, there is route via city C such that AC$\perp $CB, AC = 2x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of highway.

$AC=2xkm\phantom{\rule{0ex}{0ex}}CB=2(x+7)km\phantom{\rule{0ex}{0ex}}ABisthehighway\phantom{\rule{0ex}{0ex}}AB=26km\phantom{\rule{0ex}{0ex}}Applyingpythagorastheoremin\u2206ABC\phantom{\rule{0ex}{0ex}}A{B}^{2}=C{B}^{2}+A{C}^{2}\phantom{\rule{0ex}{0ex}}{26}^{2}={\left[2(x+7)\right]}^{2}+{\left(2x\right)}^{2}\phantom{\rule{0ex}{0ex}}676=4\left({x}^{2}+14x+49\right)+4{x}^{2}\phantom{\rule{0ex}{0ex}}{x}^{2}+14x+49+{x}^{2}=169\phantom{\rule{0ex}{0ex}}2{x}^{2}+14x-120=0\phantom{\rule{0ex}{0ex}}{x}^{2}+7x-60=0\phantom{\rule{0ex}{0ex}}{x}^{2}+12x-5x-60=0\phantom{\rule{0ex}{0ex}}\left(x+12\right)(x-5)=0\phantom{\rule{0ex}{0ex}}x=5\left[\mathrm{sin}cexisthelengthofapathitcannotbenegativex\ne -12\right]$

Regards

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