The width of a rectangle measures left bracket, 8, c, minus, 5, right bracket(8c−5) centimeters, and its length measures left bracket, 2, c, plus, 10, right bracket(2c+10) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer
Multiple Choice Answers
24, plus, 6, c24+6c
5, plus, 10, c5+10c
12, plus, 3, c12+3c
10, plus, 20, c10+20c
The perimeter of a rectangle is found by adding up all four sides.
One side has a length of (8c-5) centimeters.
One side has a length of (2c+10) centimeters.
The other two sides are also equal to these lengths.
Therefore, the expression that represents the perimeter is:
(8c-5) + (2c+10) + (8c-5) + (2c+10) = 20c + 10.
So the correct answer is 20c + 10.
The formula to calculate the perimeter of a rectangle is given by the expression:
Perimeter = 2(length + width)
In this case, the length is (2c + 10) and the width is (8c - 5).
Therefore, the expression representing the perimeter of the rectangle is:
2(2c + 10 + 8c - 5)
Simplifying the expression:
2(10c + 5)
Finally, the perimeter expression is:
20c + 10.
To find the perimeter of the rectangle, we need to add up all the sides.
The width of the rectangle is given as (8c−5) centimeters and the length is given as (2c+10) centimeters.
The perimeter is the sum of all four sides of the rectangle.
The two sides of length are (2c+10) and (2c+10) which adds up to 2(2c+10) or 4c + 20.
The two sides of width are (8c−5) and (8c−5) which adds up to 2(8c−5) or 16c − 10.
Finally, we can find the perimeter by adding the lengths of all four sides:
Perimeter = (4c + 20) + (16c − 10)
Simplifying the expression gives:
Perimeter = 4c + 20 + 16c − 10
Perimeter = 20c + 10
So the expression that represents the perimeter of the rectangle is 20c + 10.
Therefore, the correct answer is: 10, plus, 20, c (10+20c).