Final answer:
The question gave a perimeter of 90 meters for a rectangular garden with the width as '2n + 5' and the length as 'twice the width.' Solving for 'n' in the perimeter equation gives a width of 15 meters and a length of 30 meters. Calculating the area yields 450 square meters, which does not match any of the given options, suggesting an error in the question or options.
Step-by-step explanation:
Margo has a rectangular garden where the length is twice the width, and we are given that the perimeter is 90 meters and the width is 2n + 5 meters. To find the area of the garden, we first need to establish expressions for both the width and the length. We know that the perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Given that the length is twice the width, we can write l = 2(2n+5) = 4n + 10.
So, the perimeter can be expressed as:
90 = 2(4n + 10) + 2(2n + 5)
This simplifies to:
90 = 8n + 20 + 4n + 10
Combining like terms gives us:
90 = 12n + 30
Subtracting 30 from both sides, we get:
60 = 12n
Dividing by 12 gives us:
n = 5
Now that we have the value for n, we can find the width by substituting n into the width expression:
w = 2n + 5 = 2(5) + 5 = 15 meters
The length, being twice the width, is:
l = 4n + 10 = 4(5) + 10 = 30 meters
Now we can calculate the area (A) of the rectangle:
A = l × w = 30 meters × 15 meters = 450 square meters
However, this does not match with any of the options given in the multiple choice (A, B, C, D). Therefore there must be a mistake either in the question or the provided options, as calculation with the given values does not lead to any of the provided solutions.To determine the area of the rectangular garden, we need to know the length and width of the garden. It is given that the length is twice the width, and the width is 2n + 5.Let's solve for the width using the given information about the perimeter. The perimeter is the sum of all sides of the rectangle, which in this case is 2 times the length plus 2 times the width. The perimeter is given as 90, so: