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 dimensions that will maximize the area of the rectangular garden, we need to understand the given information. Mrs. hs has 40 yards of fencing, and she plans to use part of the 26-yard wall of her house as one side of the garden.

Let's break down the problem step by step:

1. Length of the Garden (L):
Since Mrs. hs plans to use part of the 26-yard wall of her house as one side, the remaining length of the garden can be calculated as:
L = 40 - 26 = 14 yards

2. Width of the Garden (W):
With only two remaining sides to be fenced, we can divide the available fencing equally for the length and width, as the perimeter of a rectangle is given by P = 2L + 2W. In this case, the perimeter is equal to the available fencing:
2L + 2W = 40
2(14) + 2W = 40
28 + 2W = 40
2W = 40 - 28
2W = 12
W = 12/2
W = 6 yards

Therefore, the dimensions of the garden should be 14 yards for the length and 6 yards for the width, resulting in a rectangular garden that measures 14 yards by 6 yards.

To calculate the area and answer the remaining questions:

3. Area of the Garden:
The area of a rectangle is given by A = L * W, where A represents the area, L represents the length, and W represents the width.
A = 14 * 6 = 84 square yards

4. Area in Square Feet:
Since 1 yard is equal to 3 feet, we can convert the area from square yards to square feet by multiplying by the conversion factor (3 * 3 = 9, since we are converting 2-dimensional measurements):
Area in square feet = 84 * 9 = 756 square feet.

5. Explanation of How These Dimensions Maximize the Area:
The dimensions of 14 yards by 6 yards were chosen because they allocated the available fencing most effectively. By using the longer side for the length and the shorter side for the width, we maximize the area of the rectangle. Any other combination of dimensions would result in a smaller area because it would use the fencing less efficiently.

Hence, Mrs. hs should use the dimensions of 14 yards by 6 yards for her garden, resulting in an area of 84 square yards or 756 square feet.