Answer:
x = 5
Explanation:
The area of the rectangle can be found by multiplying length x width:
Total Area = 55:
Length = x + 6
Width = x
Set the equation:
(x)(x + 6) = 55
First, distribute x to all terms within the parenthesis:
(x)(x + 6) = x² + 6x = 55
Next, set the equation equal to 0. Subtract 55 from both sides of the equation:
x² + 6x (-55) = 55 (-55)
x² + 6x - 55 = 0
Then, solve for x. Find factors of x² and -55 that, when combined, will result in 6x:
x² + 6x - 55 = 0
x 11
x -5
(x + 11)(x - 5) = 0
Then, solve each individual parenthesis:
(x + 11) = 0
x + 11 (-11) = 0 (-11)
x = -11
(x - 5) = 0
x - 5 (+5) = 0 (+5)
x = 5
Note, however, that a side cannot have a negative measurement. Therefore, x = 5 is your only answer.
~