Question

Question 12:-
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
​

Answer 1

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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