Question

A playground is 50-feet long by 30-feet wide. The length and width of the playground will each be increased by the same number of feet. The following expression represents the perimeter of the larger playground:
(x + 50) + (x + 30) + (x + 50) + (x + 30)

Which expression is equivalent to the expression for the perimeter of the larger playground?
A) (x + 50) + (x + 30)
B) 4x + 40
C) 4(x + 40)
D) 4(x + 160)

Answer 1

Answer:

Option C is correct

4(x+40)

Step-by-step explanation:

Perimeter(P) of rectangle is given by:

$P = 2(l+w)$

where, l is the length and w is the width of the rectangle.

As per the statement:

A playground is 50-feet long by 30-feet wide.

The length and width of the playground will each be increased by the same number of feet.

The following expression represents the perimeter of the larger playground is:

(x + 50) + (x + 30) + (x + 50) + (x + 30)

first Remove parenthesis:

x + 50+ x + 30 + x + 50+ x + 30

Combine like terms;

4x+160

using distributive property  $a \cdot (b+c) = a\cdot b+ a\cdot c$ we have

⇒4(x+40)

Therefore, the expression is equivalent to the expression for the perimeter of the larger playground is, 4(x+40)

Answer 2

The answer is C
You can ignore the parenthesis so you have
x + 50 + x + 30 + x + 50 + x + 30          (combine like terms)
4x+160                                                  (factor out the 4)
4(x+40)