A rectangle is 12 cm longer than it is wide. a wooden walk 2 ft wide is placed around the pond. the area covered by the pond and walk is 160 ft^2 greater than the area covered by the pond alone. What are the dimensions of the pond
I suspect that the pond is 12 ft longer than it is wide. 12 cm is a ridiculous amount. Assuming that, we have the dimensions of w and w+12.
Then we are told that
(w+4)(w+12+4) - (w)(w+12) = 160
Solve that and you find w=12.
So, the pond is 12x24
16*28 - 12*24 = 160
To find the dimensions of the pond, we can set up an equation using the information given.
Let's assume that the width of the pond is x cm.
According to the problem, the rectangle is 12 cm longer than it is wide. So the length of the rectangle (which represents the length of the pond) would be (x + 12) cm.
The wooden walk is placed 2 ft (or 24 inches) wide around the pond. To find the area covered by both the pond and the walk, we need to add 24 inches to each dimension of the pond.
So the width of the covered area would be (x + 24) cm, and the length of the covered area would be ((x + 12) + 24) cm, which simplifies to (x + 36) cm.
Now, according to the problem, the area covered by the pond and walk is 160 ft^2 greater than the area covered by the pond alone.
To find the area of the pond alone, we multiply the width by the length:
Area of the pond = x cm * (x + 12) cm = x^2 + 12x cm^2
Similarly, to find the area covered by the pond and walk, we multiply the width by the length:
Area of the pond and walk = (x + 24) cm * (x + 36) cm = (x^2 + 60x + 864) cm^2
According to the problem, the area covered by the pond and walk is 160 ft^2 greater than the area covered by the pond alone. We can convert the area from cm^2 to ft^2 by dividing by the conversion factor, which is 929.03 cm^2/ft^2:
(x^2 + 60x + 864) cm^2 - (x^2 + 12x) cm^2 = 160 ft^2 * 929.03 cm^2/ft^2
(x^2 + 60x + 864 - x^2 - 12x) cm^2 = 160 * 929.03 cm^2
48x + 864 cm^2 = 148644.8 cm^2
48x = 147780.8 cm^2
x ≈ 3075.6 / 48 ≈ 64 cm
So, the width of the pond is approximately 64 cm.
The length of the pond would be (64 + 12) cm = 76 cm.
Therefore, the dimensions of the pond are approximately 64 cm by 76 cm.