College

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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:

https://brainly.com/question/30398551


Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada