The length of a rectangle is twice the width. The area is 578 yd.^2. Find the length and width.
Width = X-yds.
Length = 2X-yds.
Area = 2X * X = 578 yds^2.
2x^2 = 578,
x^2 = 289,
X = 17 yds.
2X = 2*17 = 34 yds.
I'm like a rectangle without any curves, straight to the point! Let's solve this riddle together.
Let's assume the width of the rectangle is "x" yards, so the length would be 2 times that, making it 2x yards.
Now we can use the formula for finding the area of a rectangle, which is length times width. In this case, the area is given as 578 square yards, so we have:
x * 2x = 578
2x^2 = 578
Now, let's divide both sides of the equation by 2 to solve for x^2:
x^2 = 578 / 2
x^2 = 289
Taking the square root of both sides:
x = √289
So, the width of the rectangle is x = 17 yards.
And since the length is twice the width, the length would be 2x = 2 * 17 = 34 yards.
Voila! The length of the rectangle is 34 yards and the width is 17 yards.
Step 1: Assign variables
Let's assign variables to the length and width of the rectangle.
Let's say the width is represented by 'w'.
Since the length is twice the width, the length can be represented by '2w'.
Step 2: Use the formula for the area of a rectangle
The area of a rectangle is given by the formula: Area = Length * Width.
Step 3: Plug in the given information
We are given that the area is 578 square yards. So we can write the equation as: 578 = (2w) * w.
Step 4: Solve the equation
Multiply 2w and w: 578 = 2w^2.
Divide both sides of the equation by 2: 289 = w^2.
To solve for w, take the square root of both sides of the equation: w = ±√289.
Step 5: Determine the width
Since width cannot be negative, we only consider the positive square root: w = √289 = 17.
Step 6: Determine the length
Since the length is twice the width, length = 2w = 2 * 17 = 34.
Step 7: Answer
The length of the rectangle is 34 yd and the width is 17 yd.
To find the length and width of the rectangle, we can set up a system of equations based on the given information.
Let's assume the width of the rectangle is "w" yards. Since the length is twice the width, we can express the length as "2w" yards.
Now, we can use the formula for the area of a rectangle, which is length multiplied by width. According to the question, the area is given as 578 yd², so we have:
2w * w = 578
Simplifying this equation, we have:
2w² = 578
Next, we can divide both sides of the equation by 2 to isolate w²:
w² = 289
Now, we can take the square root of both sides to solve for w:
√(w²) = √289
w = ±17
Since the width of a rectangle cannot be negative, we discard the negative value. Therefore, the width is 17 yards.
To find the length, we substitute the value of the width back into one of our earlier expressions:
length = 2w = 2 * 17 = 34 yards
So, the length of the rectangle is 34 yards, and the width is 17 yards.