A rectangular park has an area of 2/3 square mile. The length of the park is 2 2/3 the width of the park. What is the width of the park?
I am confused on how to do this. I know lw=a
A= 2/3 sq mi
l= 2 2/3w
but I do not understand how to find the width :/
Haha
That is not good
To find the width of the park, we can use the given information and the formula for the area of a rectangle, which is length multiplied by width (lw = a).
Here's how you can solve the problem step by step:
Step 1: Let's assign variables:
Let w represent the width of the park.
Step 2: Express the length in terms of the width:
The problem states that the length of the park is 2 2/3 times the width.
So, the length is (2 2/3)w.
Step 3: Write down the area equation:
The area of the park is given as 2/3 square mile, so we can write:
lw = 2/3
Step 4: Substitute the values into the equation:
Substituting the expressions for length and area into the area equation, we get:
(2 2/3)w * w = 2/3
Step 5: Simplify the equation:
To simplify, we need to convert the mixed number 2 2/3 into an improper fraction.
2 2/3 is equivalent to (8/3)w.
The equation becomes:
(8/3)w * w = 2/3
Step 6: Solve for w:
Multiply both sides of the equation by 3 to eliminate the denominators:
8w^2 = 2
Divide both sides of the equation by 8:
w^2 = 2/8
w^2 = 1/4
Take the square root of both sides to solve for w:
w = √(1/4)
w = 1/2
So, the width of the rectangular park is 1/2 mile.
A = LW
A = 2/3
L 2 2/3
2/3 = 8/3W
2/3 *3/8 = 3/8(8/3W)
1/4 = W