The width of a rectangle measures left bracket, 5, v, minus, w, right bracket(5v−w) centimeters, and its length measures left bracket, 6, v, plus, 8, w, right bracket(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
To find the perimeter of a rectangle, we need to add up the lengths of all four sides.
The width of the rectangle is (5v-w) centimeters, so the two widths add up to 2*(5v-w) = 10v-2w centimeters.
The length of the rectangle is (6v+8w) centimeters, so the two lengths add up to 2*(6v+8w) = 12v+16w centimeters.
The perimeter of the rectangle is then the sum of the two widths and the two lengths, so the expression for the perimeter is:
(10v-2w) + (12v+16w) = 22v + 14w centimeters.
To find the perimeter of a rectangle, we add up the lengths of all its sides.
The rectangle has two pairs of equal sides: the top and bottom sides are each \(5v - w\) cm long, and the left and right sides are each \(6v + 8w\) cm long.
We can find the perimeter by adding up all four sides:
\(P = (5v - w) + (5v - w) + (6v + 8w) + (6v + 8w)\)
Combining like terms, we get:
\(P = 10v - 2w + 14v + 16w\)
Simplifying further, we have:
\(P = 24v + 14w\)
Therefore, the expression that represents the perimeter is \(24v + 14w\) centimeters.
To find the perimeter of a rectangle, we need to calculate the sum of all its sides.
Given that the width measures (5v−w) centimeters and the length measures (6v+8w) centimeters, we can express the perimeter as:
P = 2*(width + length)
Substituting the given expressions for width and length:
P = 2*((5v−w) + (6v+8w))
Now, simplify the equation:
P = 2*(5v - w + 6v + 8w)
Combine like terms:
P = 2*(11v + 7w)
Finally, simplify the expression:
P = 22v + 14w
Therefore, the expression that represents the perimeter of the rectangle is 22v + 14w centimeters.