The figures below are similar.

What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.

1. 8/2 and 49/4
2. 7/2 and 49/4
3. 7/2 and 9/4
4. 8/3 and 9/4

Question

The figures below are similar. 

What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.

1. 8/2 and 49/4
2. 7/2 and 49/4
3. 7/2 and 9/4
4. 8/3 and 9/4

anonymous · Answer

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anonymous · Answer

@mathmale  I know that it's either 2 or 3 because the ratio of the sides are 7:2 but I remember them teaching us a formula to find the ratio of the areas, but I forgot it >.<

mathmale · Answer

We are given two SIMILAR polygons, and see that the lengths of the bottom edges are given:  Let's focus on the PERIMETERS only.  In terms of LARGER to SMALLER perimeters, the relevant ratio is $$\frac{ 28~yd }{ 8 ~yd }$$  This last result should be reduced.  Would you do that now, please?

mathmale · Answer

You've already done that calculation, but do it again, please.

anonymous · Answer

$$\frac{ 7 yd }{ 2yd }$$

mathmale · Answer

Because you've done this correctly, we can eliminate choices 1 and 4.   (Do cancel the units "yd".)

anonymous · Answer

Honestly, the larger triangle's area doesn't "look" as big as 49:4 but it says it is not drawn to scale and plus I would like to go on more than just a hunch.

mathmale · Answer

A method of finding the ratio of the areas doesn't come to my mind immediately either.
However, you could quickly sketch these two similar polygons more to scale (7 to 2) and then estimate how the areas are related.   It's hard to see this relationship when the drawings are not to scale.

anonymous · Answer

Thanks! From what I can tell, it far more resembles 9/4.

mathmale · Answer

Since every dimension of the larger poly would be 3.5 times the corresponding dimension in the smaller, you could assume that the height of the larger (even if not specifically shown) is 3.5 times greater than that of the smaller. 

that's one way to arrive at an answer.

Drawing these polygons to scale is not "acting on a hunch."  Are you willing to do that?

The larger will have every dimension 3.5 times larger than the corresponding dimension of the smaller.

anonymous · Answer

@mathmale i need help with my question

mathmale · Answer

Are you satisfied with these two approaches (first, drawing the 2 polygons to scale) and second, doing a numerical estimation?   

For example, you could say that the area of the larger poly is roughly 28 by 30 yards, and that of the smaller is roughly 8 by 30/3.5 yards.

mathmale · Answer

Estimation, combined with the concept of geometric similarity, is the key to solving this problem.

anonymous · Answer

Thanks! the answer is 2. 7/2 and 9/4