Question

After the construction of the bypass road the distance saved in reaching Barogh from Alwah

will be​

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 :

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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