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Answer :
Final answer:
The problem can be solved using algebraic equations. We find a quadratic equation for width (w) which gives us a positive value of 6 yards. Substituting this in the length's equation gives us the length as 20 yards.
Explanation:
This problem can be solved using Algebra. First, we know that the area of a rectangle is found by multiplying its length (l) by its width (w). Therefore, we can set up the equations: lw = 120 square yards and l = 2w + 8 yards.
We can substitute the second equation into the first to get: (2w + 8)w = 120. This simplifies to 2w^2 + 8w - 120 = 0, a quadratic equation.
Solving the quadratic equation, we find the possible values for w to be 6 and -10. We discard -10 as width can't be negative, thus the width of the rectangle is 6 yards. Substituting this value in l = 2w + 8, we calculate the length to be 20 yards.
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