Question

Write two expressions for the perimeter of the figure.

Note: The figure is not drawn to scale.
(a) Use all four side lengths.

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

Answer 1

• a) 18x + 9x + 4x + 16
• b) 31x + 16

Given :

• 4 sides and their lengths

To find :

• The perimeter

Solution :

we know that,

• The perimeter of a shape is the sum of all of it's sides
• Perimeter of the given shape = 18x + 16 + 4x + 9x
• Perimeter of the given shape = 31x + 16

Thus, the perimeter of the given figure would be 31x + 16 .

Answer 2

`\textsf{(a)} \quad \textsf{Perimeter} = \boxed{18x}+\boxed{16}+\boxed{4x}+\boxed{9x}`

`\textsf{(b)}\quad \textsf{Perimeter}=\boxed{31x+16}`

Explanation:

The perimeter of a two-dimensional shape is the sum of the lengths of its outer edges. Therefore, for the given four-sided figure, the perimeter is the sum of its four side lengths:

`\textsf{Perimeter} = \boxed{18x}+\boxed{16}+\boxed{4x}+\boxed{9x}`

We can simplify the expression by combining like terms:

`\begin{aligned}\textsf{Perimeter} &= 18x+16+4x+9x\\&=18x+9x+4x+16\\&=\boxed{31x+16}\end{ailgned}`