The area of a playground is 64 square yards. The length of the playground is 4 times longer than its width. How can I solve this?
A = LW
64 = 4W * W
64 = 4W^2
16 = W^2
4 = W
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To solve this, you can follow these steps:
Step 1: Let's assume the width of the playground is "w" yards.
Step 2: According to the given information, the length of the playground is 4 times longer than its width. So, the length would be "4w" yards.
Step 3: To find the area of the playground, we use the formula: area = length × width.
Step 4: Substituting the values, the area of the playground is calculated as: area = (4w) × w.
Step 5: Simplifying the equation further, the area is: area = 4w².
Step 6: The area of the playground is given as 64 square yards. So, the equation becomes: 4w² = 64.
Step 7: Dividing both sides of the equation by 4, we get: w² = 16.
Step 8: Taking the square root of both sides of the equation, we find: w = 4.
Step 9: Thus, the width of the playground is 4 yards.
Step 10: Since the length is 4 times longer than the width, the length is: 4 × 4 = 16 yards.
Step 11: Hence, the width is 4 yards and the length is 16 yards, and the area is 64 square yards.
To solve this, we can set up an equation based on the given information. Let's denote the width of the playground as "w".
Since the length of the playground is 4 times longer than its width, the length would be 4w.
The area of the playground is given as 64 square yards. The formula for finding the area of a rectangle is length × width.
So, we can set up the equation: 4w × w = 64.
Simplifying the equation, we have: 4w^2 = 64.
To solve for w, divide both sides of the equation by 4: w^2 = 16.
Taking the square root of both sides, we get: w = √16.
Thus, w = 4.
So, the width of the playground is 4 yards.
To find the length, we can substitute the width value back into the equation: Length = 4w = 4 × 4 = 16 yards.
Therefore, the length of the playground is 16 yards.