Answer :
Final answer:
The length of the lawn is 30 feet and the width is 4 feet.
Explanation:
Let x be the width of the lawn.
According to the problem, the length is 10 feet more than five times the width, so the length is 5x+10.
The area of a rectangle is given by the formula length times width, so we have the equation:
(5x+10)(x) = 120
Expanding and simplifying the equation gives us:
5x^2 + 10x = 120
Now, let's solve the quadratic equation:
5x^2 + 10x - 120 = 0
Dividing the equation by 5 to simplify it gives us:
x^2 + 2x - 24 = 0
Factoring the quadratic equation gives us:
(x+6)(x-4) = 0
Therefore, the possible values for the width are -6 and 4, but the width cannot be negative, so the width of the lawn is 4 feet.
Substituting this value back into the equation for the length gives us:
Length = 5x+10 = 5(4)+10 = 20+10 = 30 feet.
Therefore, the length of the lawn is 30 feet and the width is 4 feet.
Learn more about Solving quadratic equations here:
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