Simon and Jane have rectangular-shaped vegetable gardens. The width of Jane’s garden is double the width of Simon’s garden. The area of Jane’s garden is 4 times that of Simon’s garden. Which statement is true?
Answer
A. Jane’s garden has the same perimeter as Simon’s garden.
B. The length of Jane’s garden is double the length of Simon’s garden.
C. The perimeter of Jane’s garden is four times that of Simon’s garden.
D. The length of Jane’s garden is four times the length of Simon’s garden.
the answer is B. length of jane's garden is double the length of simon's
garden
To determine which statement is true, we need to compare the dimensions and characteristics of both Simon's and Jane's gardens.
Let's start by assigning variables to the dimensions of Simon's garden. Let's say the length is Ls and the width is Ws. Since the width of Jane's garden is double the width of Simon's garden, we can say that Wj = 2Ws.
We are also given that the area of Jane's garden is 4 times that of Simon's garden. We can set up the equation for this: Aj = 4As, where Aj is the area of Jane's garden and As is the area of Simon's garden. The area of a rectangle is given by multiplying its length and width, so we have Lj * Wj = 4 * (Ls * Ws).
Now, let's analyze each statement and see which one is true:
A. Jane’s garden has the same perimeter as Simon’s garden.
To determine the perimeter, we need to add up all the sides of the rectangle. The perimeter of Simon's garden is given by Ps = 2 * (Ls + Ws), and the perimeter of Jane's garden is Pj = 2 * (Lj + Wj). Since we don't have any information about the lengths of the gardens, we cannot determine if this statement is true.
B. The length of Jane’s garden is double the length of Simon’s garden.
From the given information, we don't have any details about the length of Simon's or Jane's garden. Therefore, we cannot determine if this statement is true.
C. The perimeter of Jane’s garden is four times that of Simon's garden.
As mentioned earlier, the perimeter of Simon's garden is Ps = 2 * (Ls + Ws), and the perimeter of Jane's garden is Pj = 2 * (Lj + Wj). Since we know that Wj = 2Ws, we can substitute it into the equation to get Pj = 2 * (Lj + 2Ws). The perimeter of Jane's garden is not four times that of Simon's garden. Therefore, this statement is false.
D. The length of Jane’s garden is four times the length of Simon's garden.
Based on the given information, we do not have any details or relationship mentioned for the lengths of the gardens. Therefore, we cannot determine if this statement is true.
In conclusion, none of the statements are true based on the information provided.