*CONSTRUCTING A BYPASS*
While travelling from Alwah to Barogh, one crosses the busy hamlet of Chagotkar. 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.
After the construction of the bypass road the distance saved in reaching Barogh from Alwah will be
a) 10 km
b) 2 km
c) 6 km
d) 16 km
Answers
Answer:
d) 16 km
Step-by-step explanation:
I hope answer is correct
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 :
After the construction of the bypass road the distance saved in reaching Barogh from Alwah will be
a) 10 km
b) 2 km
c) 6 km
d) 16 km
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
=> (x + 15)(x - 8) = 120
=> x = 8 x can not be -ve
x = 8
x + 7 = 15
8 + 15 = 23 km
23 - 17 = 6 km
After the construction of the bypass road the distance saved in reaching Barogh from Alwah will be 6 km
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