Question

The width of a rectangle is 8c−5 centimeters, and its length is 2c+10 centimeters. What expression represents the perimeter of the rectangle?

Answer 1

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?

The perimeter of a rectangle is the sum of all of its sides:

The perimeter of a rectangle is the sum of all of its sides:

8, c, minus, 5, start subscript, width, end subscript, plus , 8, c, minus, 5, start subscript, width, end subscript, plus , 2, c, plus, 10, start subscript, length, end subscript, plus , 2, c, plus, 10, start subscript, length, end subscript

width

8c−5

​

​

+

width

8c−5

​

​

+

length

2c+10

​

​

+

length

2c+10

​

​

8, c, minus, 5, plus, 8, c, minus, 5, plus, 2, c, plus, 10, plus, 2, c, plus, 10

8c−5+8c−5+2c+10+2c+10

8, c, plus, 8, c, plus, 2, c, plus, 2, c, minus, 5, minus, 5, plus, 10, plus, 10

8c+8c+2c+2c−5−5+10+10

start underbrace, 8, c, plus, 8, c, plus, 2, c, plus, 2, c, end underbrace, start subscript, 20, c, end subscript, , start underbrace, minus, 5, minus, 5, plus, 10, plus, 10, end underbrace, start subscript, plus, 10, end subscript

20c

8c+8c+2c+2c

​

​

+10

−5−5+10+10

​

​

20, c, plus, 10

20c+10

10, plus, 20, c

10+20c

Step-by-step explanation:

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?

The perimeter of a rectangle is the sum of all of its sides:

The perimeter of a rectangle is the sum of all of its sides:

8, c, minus, 5, start subscript, width, end subscript, plus , 8, c, minus, 5, start subscript, width, end subscript, plus , 2, c, plus, 10, start subscript, length, end subscript, plus , 2, c, plus, 10, start subscript, length, end subscript

width

8c−5

​

​

+

width

8c−5

​

​

+

length

2c+10

​

​

+

length

2c+10

​

​

8, c, minus, 5, plus, 8, c, minus, 5, plus, 2, c, plus, 10, plus, 2, c, plus, 10

8c−5+8c−5+2c+10+2c+10

8, c, plus, 8, c, plus, 2, c, plus, 2, c, minus, 5, minus, 5, plus, 10, plus, 10

8c+8c+2c+2c−5−5+10+10

start underbrace, 8, c, plus, 8, c, plus, 2, c, plus, 2, c, end underbrace, start subscript, 20, c, end subscript, , start underbrace, minus, 5, minus, 5, plus, 10, plus, 10, end underbrace, start subscript, plus, 10, end subscript

20c

8c+8c+2c+2c

​

​

+10

−5−5+10+10

​

​

20, c, plus, 10

20c+10

10, plus, 20, c

10+20c

Answer 2

The expression representing the perimeter of the rectangle with width 8c−5 cm and length 2c+10 cm is 20c+10 centimeters.

Step-by-step explanation:

The question is asking for the expression that represents the perimeter of a rectangle. To find the perimeter of a rectangle, we use the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that the width (w) is 8c−5 centimeters and the length (l) is 2c+10 centimeters, we substitute these expressions into the formula.

Therefore, the perimeter of the rectangle is:

P = 2(2c+10) + 2(8c−5)

P = 4c + 20 + 16c - 10

P = 20c + 10

So, the expression that represents the perimeter of the rectangle is 20c + 10 centimeters.