Question

what is the perimeter of the figure shown below, which is not drawn to scale?

a ( 5x + 33 ) b ( 5x^2 + 33 )
c ( 5x + 30 ) d ( 8x^2 + 30 )

Explanation:

Step1: Find the missing vertical side

The vertical side on the right - hand side: \(3x+(3x + 2-(3x))=3x + 2\) (by comparing the left - hand side vertical length \(3x + 2\) with the known vertical segments).

Step2: Find the missing horizontal side

The horizontal side: \((x + 13)+8-(x + 5)=x+13 + 8-x - 5=16\) (by comparing the top - most horizontal length \(x + 13\) and the bottom - most horizontal length \(x + 5\)).

Step3: Calculate the perimeter

The perimeter \(P=(x + 13)+(3x)+8+2+(x + 5)+(3x + 2)+(3x + 2-(3x))+((x + 13)+8-(x + 5))\)

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Another way: Using the property of translation (shifting the sides to form a rectangle - like shape for perimeter calculation).
The sum of the horizontal sides: \((x + 13)+(x + 5)+8=2x+26\)
The sum of the vertical sides: \((3x + 2)+3x+2=6x+4\)
The perimeter \(P = 2\times(\text{sum of non - parallel adjacent sides})\) (after translation, we can think of it as a rectangle - like figure with two pairs of parallel sides).

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Answer:

\(8x + 30\) (It seems there is a typo in the original options. If we assume the intended answer is from the given options, and there was a mis - writing in the problem setup, but following the correct algebraic perimeter calculation for the given side lengths, the perimeter is \(8x+30\))