a swimming pool has an area of 40 square metres and a perimeter of 26 metres what is the length and width of the swimming pool and is it possible for a pool to have the same area but a larger perimeter?

To find the length and width of the swimming pool, we can set up a system of equations using the given values.

Let's assume the length of the pool is L and the width is W.

We are given two pieces of information:
1. The area of the pool is 40 square meters: A = L * W = 40
2. The perimeter of the pool is 26 meters: P = 2L + 2W = 26

Using the first equation, we can solve for one variable in terms of the other variable:
L = 40 / W

Substitute this value for L in the second equation:
2(40 / W) + 2W = 26

Multiply both sides by W to get rid of the fraction:
80 + 2W^2 = 26W

Rearrange the equation to a quadratic form:
2W^2 - 26W + 80 = 0

Now we can solve this quadratic equation. Factoring does not work, so we can use the quadratic formula:
W = [-(-26) ± sqrt((-26)^2 - 4(2)(80))] / (2(2))
W = (26 ± sqrt(676 - 640)) / 4
W = (26 ± sqrt(36)) / 4
W = (26 ± 6) / 4

Solving for W yields two possible values: W = 8 or W = 5/2 (2.5)

Using these values, we can find the corresponding lengths:

If W = 8:
L = 40 / 8 = 5

If W = 5/2 (2.5):
L = 40 / (5/2) = 16

So the two possible sets of length and width are:
1. Length = 5 meters, Width = 8 meters
2. Length = 16 meters, Width = 2.5 meters

Regarding the second part of your question, it is not possible for a pool to have the same area but a larger perimeter than the given pool. The perimeter depends on the lengths of all sides, while the area depends on the product of the length and width. So if the area remains constant, the length and width will have to change accordingly, resulting in a change in perimeter as well.

To find the length and width of the swimming pool, we can set up a system of equations using the given information.

Let's assume the length of the pool is L and the width is W.

1. Area equation: We know that the area of a rectangle is given by length multiplied by width. So, we have the equation:
L * W = 40

2. Perimeter equation: The perimeter of a rectangle is given by the sum of all its sides. For our rectangle, this is:
2L + 2W = 26

Now we can solve this system of equations to find the values of L and W.

First, let's solve the area equation for one of the variables. We can solve for L by dividing both sides of the equation by W:
L = 40 / W

Next, substitute this value of L into the perimeter equation:
2(40 / W) + 2W = 26

Now we simplify and solve for W:
80 / W + 2W = 26
80 + 2W^2 = 26W
2W^2 - 26W + 80 = 0

We can solve this quadratic equation to find the possible values for W. Factoring this equation or using the quadratic formula will give you two solutions for W.

After obtaining the values for W, substitute them back into the area equation (L * W = 40) to find the corresponding lengths.

Regarding whether a pool can have the same area but a larger perimeter, the answer is no. The perimeter of a rectangle is directly related to the length and width, as shown in the perimeter equation (2L + 2W = 26). If the area remains the same, there is only one possible combination of lengths and widths that satisfy the equation, and the perimeter will also remain constant.

W * L = 40

L = 40 - W

2L + 2W = 26

Substitute 40-W for L in the third equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.

For the last question, try halving one of the dimensions.