College

The area of a rectangular lawn is 120 square feet. The length is 10 feet more than five times the width. Find the length and the width of the lawn.

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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