A rectangle with an area of 294 square feet has a length and width in a ratio of 3:2. What are the length and width?length = feetwidth = feet
Question
Solution
To find the length and width of the rectangle, we first need to understand that the area of a rectangle is found by multiplying its length by its width.
Given that the area is 294 square feet and the ratio of length to width is 3:2, we can set up the following equation:
(3x) * (2x) = 294
Solving this equation will give us the values of length and width.
Step 1: Simplify the equation:
6x^2 = 294
Step 2: Divide both sides by 6:
x^2 = 49
Step 3: Take the square root of both sides:
x = 7
Now that we have the value of x, we can find the length and width:
Length = 3x = 37 = 21 feet Width = 2x = 27 = 14 feet
So, the length of the rectangle is 21 feet and the width is 14 feet.
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