An artificial lake is in the shape of a rectangle and has an area of \(\frac{9}{20}\) square mile. The width of the lake is \(\frac{1}{5}\) the length of the lake. What are the dimensions of the lake?
Answer (3)
The area is width times length, so you'd divide the area by the width. This is 9/20 divided by 1/5. When dividing fractions, you flip the second number then divide straight across. This would be 9/20 x 5/1. You'd get 45/20, or in mixed number form, 2 and 1/4.
To solve this problem, we'll first need to define our variables. Let's let L represent the length of the lake and W represent the width of the lake. According to the problem, W is 1/5 the length of L, or W = L/5. The area of the lake (A) is given as 9/20 square miles.
Since area A is the product of length and width, A = L * W. Using the given information, we have the equation:
9/20 = L * (L/5)
Multiplying both sides of the equation by 5 to get rid of the fraction in the width (W), we get:
45/20 = LĀ²
Dividing both sides by 5/20 simplifies to:
LĀ² = 9
Taking the square root of both sides, we find:
L = 3 (since dimensions can't be negative)
Now that we have the length, we can find the width:
W = L/5
W = 3/5
Therefore, the dimensions of the lake are:
Length = 3 miles
Width = 3/5 miles
The dimensions of the artificial lake are a length of 1.5 miles and a width of 0.3 miles. The length is derived from the area equation and the relationship between the length and width. Using a step-by-step approach, we substituted into the area formula to find the dimensions.
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