After the construction of the bypass road the distance saved in reaching Barogh from Alwah
will bea) 10 km
b) 2 km
c) 6 km
d) 16 km
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 :
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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