Question

write two expressions for the perimeter of the figure.
note: the figure is not drawn to scale.
(a) use all five side lengths.
perimeter = \\(\square + \square + \square + \square + \square\\)
(b) simplify the expression from part (a).
perimeter = \\(\square\\)

Explanation:

Part (a)

Step1: Recall perimeter definition

Perimeter of a polygon is the sum of all its side lengths. The figure has five sides with lengths \(2x\), \(2\), \(16x\), \(19\), and \(6x\).

Step2: Write the sum of all sides

So, perimeter \(= 2x + 2 + 16x + 19 + 6x\) (the order of addition can be adjusted, but these are the five side lengths).

Part (b)

Step1: Combine like terms

First, combine the \(x\)-terms: \(2x + 16x + 6x = (2 + 16 + 6)x = 24x\).

Step2: Combine constant terms

Then, combine the constant terms: \(2 + 19 = 21\).

Step3: Write the simplified expression

So, the simplified perimeter is \(24x + 21\).

Answer:

(a) perimeter \(= \boldsymbol{2x} + \boldsymbol{2} + \boldsymbol{16x} + \boldsymbol{19} + \boldsymbol{6x}\) (order of the terms can vary as long as all five sides are included)
(b) perimeter \(= \boldsymbol{24x + 21}\)