Question

Can someone please answer this?

Answer 1

Let P be the pole to be erected and A, B be the opposite fixed gates. Given, PA – PB = 7Let PA = a, PB = b Hence a – b = 7 ⇒ a = 7 + b �...(1) In right ΔPAB, AB2 = AP2 + BP2 (By Pythagoras theorem) 132 = a2 + b2 169 = (7 + b)2 + b2 169 = 49 + 14b + 2b2 2b2 + 14b – 120 = 0 b2 + 7b – 60 = 0b2 + 12b - 5b – 60 = 0 b(b + 12) - 5(b + 12) = 0 (b + 12)(b – 5) = 0 Hence b = 5 or – 12
But ‘b’ cannot be negative Therefore, b = 5⇒ a = 7 + 5 = 12 Hence, PA = 12 m and PB = 5 m


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