SOLUTION: a rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. if the diagonal path across the lot is 64 feet what is the length of the two sides of th

Algebra ->  Pythagorean-theorem -> SOLUTION: a rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. if the diagonal path across the lot is 64 feet what is the length of the two sides of th      Log On


   

Question 742447: a rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. if the diagonal path across the lot is 64 feet what is the length of the two sides of the walk? Round answer to two decimal places.
Answer by lwsshak3(11628) About Me  (Show Source):
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a rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. if the diagonal path across the lot is 64 feet what is the length of the two sides of the walk? Round answer to two decimal places.
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Adjacent sides represent two legs of a right triangle with hypotenuse=64 feet
let x=length of one of the sides
89-x=length of other side
x^2+(89-x)^2=64^2
x^2+89^2-178x+x^2=4096
2x^2+7921-178x=4096
2x^2-178x+3825=0
solve for x using quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=2, b=-178, c=3825
x=36.27
or
x=52.73
length of the two sides of the walk: 36.27 ft and 52.73 ft