Question

Find the perimeter of the following polygon

Answers: 38, 44, 50, or 56

Picture in comments.

Answer 1

You know that both sides are right triangles, but you don't know the hypotenuse of the right side. If you can prove both halves of the figure congruent, you can use the pythagorean theorem to find the base of one half, and from there it's addition. Do you have an idea of how you would approach that? @kittycatkathryn

Answer 2

I have no clue where to even start. Math and I don't agree :/

Answer 3

lol OK. Do you know the triangle congruence theorems? Let's start there.

Answer 4

There are several ways to prove triangles congruent. The one to use in this instance is side-angle-side. The triangles share a side, and we know that their bases are congruent. The angle that the sides create must both be right angles (to add up to 180 degrees).
Do tell me if I've lost you @kittycatkathryn

Answer 5

We know, then that the other hypotenuse must also be 17 units long.

Answer 6

Once you find that, you should be able to find the base of those right triangles using the pythagorean formula.

Answer 7

so i add both sides to 180?

Answer 8

No, that's just to prove that the two triangles are congruent. 180 is a straight line, and for those two angles to be congruent, they must be right angles.

Answer 9

you would input the sides into:
\[a ^{2}+b ^{2}=c ^{2}\]
where c is the hypotenuse

Answer 10

but in this instance, you would want to use the form:\[c ^{2}-b ^{2}=a ^{2}\]
since you aren't trying to find the hypotenuse, but a side.

Answer 11

The result, then, should be:
\[17^{2}-15^{2}=a ^{2}\]\[289-225=a^2\]\[64=a^2\]
8=a

Answer 12

Anyway, at this point it's just addition. 17+17+16=50 or option C.
Is there anything you need more explanation with, @kittycatkathryn ?