Question

write two expressions for the perimeter of the figure.

(figure with sides 2x, 2, 16x, 19, 6x)

note: the figure is not drawn to scale.

(a) use all five side lengths.

perimeter = + + + +

(b) simplify the expression from part (a).

perimeter =

Explanation:

Step1: Identify side lengths

The five side lengths of the pentagon are \(2x\), \(2\), \(16x\), \(19\), and \(6x\). To find the perimeter using all five sides, we sum them up.
Perimeter \(= 2x + 2 + 16x + 19 + 6x\)

Step2: Simplify the expression

Combine like terms. The \(x\)-terms are \(2x\), \(16x\), and \(6x\). Their sum is \(2x + 16x + 6x = 24x\). The constant terms are \(2\) and \(19\), and their sum is \(2 + 19 = 21\). So the simplified perimeter is \(24x + 21\).

Answer:

(a) \(2x\), \(2\), \(16x\), \(19\), \(6x\) (in any order for the blanks, as addition is commutative)
(b) \(24x + 21\)