mrs.hs has 40yd of fencing to use to make a rectangular area for her garden.(she wants to keep the animals out!!!!) she pans to use part of the 26yd wall of her house as one of the sides of the rectangular area.
- what whole dimension( lengh and width) should she use for the garden so that the area is as large as possible
- what would be the area in square yards? in squeare feet?
_ how do you know the dimension you choose would have the largest area?
please can u answer all the question....this is so confusing
To find the whole dimensions that will maximize the garden's area, let's follow these steps:
1. We know that one side of the rectangular area will be the 26-yard wall of Mrs. hs' house. So, we need to find the other side of the rectangle.
2. Let's denote the other side as "x" (in yards). We also know that there are four sides, and the total fencing she has is 40 yards.
3. Since two sides of the rectangle are equal, we have: 26 + x + x + 26 = 40. Simplifying this equation, we get 2x + 52 = 40. Rearranging, we have 2x = 40 - 52, which gives us 2x = -12.
4. We encountered a problem in step 3 because we ended up with a negative value for "x". This tells us that using all 40 yards of fencing is not possible. Therefore, we need to revise our approach.
5. Instead of using all the fencing, we will use part of it to maximize the garden's area. Let's designate the length of the garden as "l" and the width as "w".
6. Since we are trying to maximize the area, we want the length and width to be as close to each other as possible. Therefore, we will assume that l = w.
7. Now, let's rewrite the equation with these new variables and the constraint. We have: 2l + 2w = 40.
8. Since l = w, we can simplify the equation to: 4w = 40.
9. Solving for w, we divide both sides by 4, which gives us: w = 40 / 4 = 10.
10. Since l = w, the length is also 10 yards.
11. To find the area, we multiply the length and width: Area = l * w = 10 * 10 = 100 square yards.
12. To convert square yards to square feet, we multiply by 9 since there are 9 square feet in 1 square yard: Area (in square feet) = 100 * 9 = 900 square feet.
13. We know that the dimension we chose (10 yards by 10 yards) has the largest possible area because we maximized the area while staying within the given constraints (using 40 yards of fencing).
Therefore, Mrs. hs should use the dimensions of 10 yards by 10 yards for her garden. The area of the garden is 100 square yards or 900 square feet. This dimension maximizes the area given the available fencing.