Question 12:-
The equation which represents the above situation algebraically is-
a) x + 73 – 120 = 0
b) x2 + 5x – 120 = 0
c) 8x + 7x - 120 = 0
d) x² + 2x - 120 = 0
Answers
Given : The road from Alwah to Chagotar, is exactly perpendicular to the road going from Chagotkar to Barogh.
The distance covered by the road between Chagotkar and Barogh is 7 kilometers more that the distance of the road connecting Alwah and Chagotkar.
Ayushi is an engineer looking after the project of building a direct bypass road that would connect Alwah and Barogh and has proposed to construct a 17 km direct bypass road between the two cities.
To Find :
The equation which represents the above situation algebraically is-
a) x² + 7x − 120 = 0
b) x² + 5x − 120 = 0
c) 8x² + 7x − 120 = 0
d) x² + 2x − 120 = 0
Solution :
Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
x² + (x + 7)² = 17²
=> x² + x² + 14x + 49 = 289
=> 2x² + 14x - 240 = 0
=> x² + 7x - 120 = 0
x² + 7x − 120 = 0 represents the situation algebraically
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