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The town Mayor plans to build a diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. If the pathway is 20 m shorter than twice the width find the length of the pathway.
The town Mayor plans to build a diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. If the pathway is 20 m shorter than twice the width find the length of the pathway.
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Answer:
Assuming length of rectangle as X, width will be (X - 20).
By pythagoras theorem,
X^2 + (X - 20)^2 = (2(X - 20)- 20)^2 =>
X^2 + X^2 - 40X + 400 = (2X - 60)^2 =>
2X^2 - 40X + 400 = 4X^2 - 240X + 3600 =>
2X^2 - 200X + 3200 = 0 =>
X^2 - 100X + 1600 = 0 =>
(X - 80)(X - 20) = 0 => X = 80 , X = 20
So the pathway should be 2(80–20)-20 = 100 metres long.
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