SOLUTION: a corner lot has an l-shaped sidewalk along its sides. The total length of the sidewalk is 17 feet. By cutting diagonally across the lot, the walking distance is shortened to 13 fe

Question 662273: a corner lot has an l-shaped sidewalk along its sides. The total length of the sidewalk is 17 feet. By cutting diagonally across the lot, the walking distance is shortened to 13 feet. What are the lengths of the two legs of the sidewalk?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a corner lot has an l-shaped sidewalk along its sides.
The total length of the sidewalk is 17 feet.
By cutting diagonally across the lot, the walking distance is shortened to 13 feet.
What are the lengths of the two legs of the sidewalk?
:
This is a pythag problem; a^2 + b^2 = c^2, where
a = one leg
b = (17-a), the other leg
c = 13
:
a^2 + (17-a)^2 = 13^2
FOIL
a^2 + 289 - 17a - 17a + a^2 = 169
Combine like terms to form a quadratic equation
2a^2 - 34a + 289 - 169 = 0
2a^2 - 34a + 120 = 0
Simplify, divide by 2
a^2 - 17a + 60 = 0
Factors to
(a-5)(a-12) = 0
a = 5, then b = 12
a = 12 then b = 5
:
:
Check on your calc: enter results: 13
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