The area of a rectangular lawn is 1,200 ft². If the length of the lawn is 27 ft less than three times its width, what is the length and the width of the lawn?
Answer (1)
Answer: The length is 48 ft and the width is 25 ftStep-by-step explanation:We are asked to find the length and width of a rectangular lawn with an area of 1,200 square feet. The problem tells us that the length of the lawn is 27 feet less than three times its width. To solve this, we first let the width be represented by x. Since the length is 27 feet less than three times the width, we can express the length as 3x - 27.Next, we recall that the formula for the area of a rectangle is length multiplied by width. Substituting the expressions we have, the equation becomes: (3x - 27) (x) = 1200Expanding this gives 3x^2 - 27w = 1200. Bringing all terms to one side, we obtain the quadratic equation 3x^2 - 27x - 1200 = 0. Dividing through by 3 simplifies it to x^2 - 9x - 400 = 0.We then solve this quadratic equation using the quadratic formula: [tex]\frac{-b ± √b^2 - 4ac}{2a}[/tex](I can’t type it here but just look at the photo as it shows the formula then just substitute the values of a, b, and c). The values of x could either be 25 of (-16). The width of a rectangle being negative is impossible, as it should be positive for it to exist. Thus, the value of the width is 25.Now that we found the width, we just need to look for the length.substitute the value of the width to the expression we made for the length: 3x - 27.L = 3(25) - 27 = 48. The length is 48.To check if the answer is correct, simply substitute the values of the length and width to the formula of the area of a rectangle = L x W.48 x 25 = 1,200.Since it matches the given area of the problem, the length and width we calculated is correct.
