Question

Find the perimeter to the figure below

Answer 1

perimeter = 6x² + 8x + 42

Explanation:

the perimeter is the sum of the 10 sides of the figure

note there are 4 sides of length (2x + 1) , 2 of (3x² + 5) and 4 of 7

then

perimeter = 4(2x + 1) + 2(3x² + 5) + 4(7)

= 8x + 4 + 6x² + 10 + 28 ← collect like terms

= 6x² + 8x + 42

Answer 2

`6x^2+8x+42`

Explanation:

The perimeter of a two-dimensional figure is the sum of the lengths of all its outer edges.

From inspection of the given figure, there are:

• Four congruent sides, each measuring (2x + 1) units.
• Four congruent sides, each measuring 7 units.
• Two congruent sides, each measuring (3x² + 5) units.

Therefore, the perimeter (P) is the sum of these side lengths:

`\begin{aligned}P&=4(2x+1)+4(7)+2(3x^2+5)\\\\&=4\cdot 2x+4\cdot 1+4\cdot 7+2\cdot 3x^2+2\cdot 5\\\\&=8x+4+28+6x^2+10\\\\&=6x^2+8x+4+28+10\\\\&=6x^2+8x+42\end{aligned}`

Therefore, the expression for the perimeter of the given figure is:

`\Large\boxed{6x^2+8x+42}`