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Q.7. For going to a city B from city A, there is route via city C such that AC 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=2x kmCB=2(x+7) kmAB is the highwayAB=26 kmApplying pythagoras theorem in ABCAB2=CB2+AC2262=2(x+7)2+2x2676=4x2+14x+49+4x2x2+14x+49+x2=1692x2+14x-120=0x2+7x-60=0x2+12x-5x-60=0x+12(x-5)=0x=5 since x is the length of a path it cannot be negative x-12


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