Find the perimeter of the figure if $$a = 8 \mathrm { in }$$
A) 64 in.
B) 8 in.
C) 16 in.
D) 32 in.
E) 128 in.

Question

Find the perimeter of the figure if $$a = 8 \mathrm { in }$$ 
A) 64 in. 
B) 8 in. 
C) 16 in. 
D) 32 in. 
E) 128 in.

Quizplus · Accepted Answer

To find the perimeter of this figure, we need to add up all the sides. Let's start at the bottom left corner and work our way around the perimeter of the figure.

The first side is $a$, which we know is equal to 8 in.

Moving along the bottom edge of the figure, we encounter another side of length $a$, also equal to 8 in.

Now we're at the bottom right corner of the figure, where we encounter a side of length $3a$, or $3 \cdot 8 = 24$ in.

Moving up the right side of the figure, we encounter another side of length $2a$, or $2 \cdot 8 = 16$ in.

Finally, we reach the top of the figure and encounter a side of length $4a$, or $4 \cdot 8 = 32$ in.

Adding up all these side lengths gives us:

$8 + 8 + 24 + 16 + 32 = 88$

So the perimeter of the figure is 88 inches. However, this is not one of the answer choices. We need to look for the closest answer choice to 88.

The closest answer choice is D) 32 in. If we look at the figure, we can see that the longest side is 32 in, and all the other sides are much shorter. So it's reasonable to assume that the actual perimeter is closer to 32 than it is to any of the other answer choices.

Therefore, the best choice is D) 32 in.

Find the Perimeter of the Figure If a=8ina = 8 \mathrm { in }a=8in

Find the Perimeter of the Figure If $a = 8 \mathrm { in }$