A rectangular pond is 10m longer than it is wide. A walk 2m wide surrounds the pond. Find the dimensions of the pond if the area of the walk is 216m2

To find the dimensions of the pond, we can set up an algebraic equation based on the given information.

Let's assume the width of the pond is "x" meters.
According to the problem, the rectangular pond is 10 meters longer than it is wide, so the length of the pond is x + 10 meters.

The area of the pond can be calculated as follows: Area = length × width
So, the area of the pond is x(x + 10) square meters.

Now, we know that a walk 2 meters wide surrounds the pond. The area of the walk is given as 216 square meters.

To find the total area of the pond and the walk, we need to add the area of the pond and twice the area of the walk (since the walk surrounds the pond on both sides):

Total Area = Pond Area + 2 × Walk Area
Total Area = x(x + 10) + 2 × 216 square meters

Simplifying further:
Total Area = x^2 + 10x + 432 square meters

Since we now have an equation for the total area, we can solve it to find the value of x (the width of the pond).

Now, we can set the equation equal to zero:
x^2 + 10x + 432 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula.
Since the equation does not easily factor, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c:
a = 1, b = 10, c = 432

x = (-(10) ± √((10)^2 - 4(1)(432))) / (2(1))
x = (-10 ± √(100 - 1728)) / 2
x = (-10 ± √(-1628)) / 2

Since we cannot take the square root of a negative number in real numbers, it means that there are no real solutions for x in this case. This implies that there is no valid width of the pond that satisfies the given conditions.

Therefore, based on the given information, there is no solution to find the dimensions of the pond.