Question 1088002: suppose a plot of land is in the shape of a right triangle. if the south border of the property is 7 miles longer than the west border and the distance between the end points is 13 miles, find the lengths of the south and west edges.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let the short leg (west side) be x.
Then, the long leg (south side) will be: x+7
And the hypotenuse, the distance between end points, is 13.
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Per Pythagoras:
sqrt(x^2 + (x + 7)^2) = 13
x^2 + (x + 7)^2 = 169
2x^2 + 14x + 49 = 169
x^2 + 7x + 49/2 = 169/2
x^2 + 7x = 60
Add 49/4 to both sides:
x^2 + 7x + 49/4 = 289/4
(x + 7/2)^2 = 289/4
Take the square root of both sides:
x + 7/2 = 17/2 or x + 7/2 = -17/2
Solve for each x and you get:
x = 5 or x = -12
Since we're not looking for a negative number, let's try the 5:
sqrt(5^2+(5+7)^2 = 13
sqrt (25+144) = 13 correct.
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