Question

Unit 3: CONSTRUCTING A BYPASS
While travelling from Alwah to Barogh, one crosses the busy hamlet of
from Alwah to Chagotar, is exactly perpendicular to the road going from
The distance covered by the road between Chagotkar and Barogh is 7 kild
distance of the road connecting Alwah and Chagotkar.
Ayushi is an engineer looking after the project of building a direct byp
connect Alwah and Barogh and has proposed to construct a 17 km direct
the two cities.
Question 11:-
Ayushi wants to represents the above situation mathematically where A rep
represents Barogh and Chagotkar is represented by C. Choose the correct fi
options given below-
(a)
A
(b)
А​

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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