SOLUTION: 1. If one side of a rectangular garden plot is three feet more than three times the other side, and the diagonal is one foot more than the longest side, what is the measure of the
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Question 331263: 1. If one side of a rectangular garden plot is three feet more than three times the other side, and the diagonal is one foot more than the longest side, what is the measure of the shortest side?
You can put this solution on YOUR website! If one side of a rectangular garden plot is three feet more than three times the other side,
and the diagonal is one foot more than the longest side, what is the measure of the shortest side?
:
Let s = the "other side";
Then
(3s+3) = "one side";
:
"the diagonal (c) is one foot more than the longest side"
c = (3s + 3) + 1
c = (3s + 4)
:
Pythag equation
s^2 + (3s+3)^2 = (3s + 4)^2
:
s^2 + 9s^2 + 18s + 9 = 9s^2 + 24s + 16
Combine like terms on the left
s^2 + 9^2 - 9s^2 + 18s - 24s + 9 - 16 = 0
:
s^2 - 6s - 7 = 0
Factors to
(s-7)(s+1) = 0
positive solution
s = 7 is the shortest side
:
:
Check solution:
7^2 + (3(7)+3))^2 = (3(7)+ 4)^2
49 + 24^2 = 25^2
49 + 576 = 625; confirms solution of s=7
