Question

find the value of x. if necessary round to the nearest tenth; it is a 3 sided triangle
a=53 sp. in.

a:10.3 in.
b:14.6 in.
c: 7.3 in.
d: 12.4 in

Answer 1

As opposed to a 4 sided triangle?

Do you mean Equilateral Triangle? All three sides are the same length?

Answer 2

yes

Answer 3

all three sides are the same length

Answer 4

Okay, what do you think? What is the area of an equilateral triangle, given then length of the sides?

Answer 5

2809

Answer 6

Perhaps this is a dumb question, but x is the length of 1 side of the triangle right?

Answer 7

correct

Answer 8

"'2809" means nothing. I'm not sure what question you were answering.

So, \(53\;in^{2} = \dfrac{\sqrt{3}}{4}x^{2}\)

Can you solve for 'x'?

Answer 9

Alright well I'll guide you with how I solved it. The first thing to know is that the area of a triangle is (1/2) * base * height.

Since it's an equilateral triangle, we know that all sides will be equal to each other.

So in order to find the height of the triangle, we should use pythagorean (may have spelled that wrong) theorem. Since the hypotenuse of the triangle is equal to x, that means to calculate the height of the triangle we need to cut the other side in half to get the height. So you end up with an equation like ((1/2)x)^2 + h^2 = x^2. Manipulate this equation to get h on one side of the equation.

Answer 10

I laud your passion, guineapig, but one can only swallow so much info at a time...

Gently... ;)

Answer 11

Alright sorry my bad lol. If this is for a high school geometry class then my way probably is too much.

Answer 12

As ever, @Compound
Your cooperation is necessary... and kinda mandatory ^_^

Make your presence felt.

Answer 13

im in algebra and their giving me this its fun

Answer 14

Then partake of the fun ^_^

Are you aware of any formula or way to get the area of an equilateral triangle when you know its side-length?

Answer 15

Ahh okay, well my method eventually reaches tk's equation, so if you want the short way just start from his equation.

Answer 16

no what is the formula?

Answer 17

So much for fun. Let's find it together.
Let us suppose this is our equilateral triangle.

Answer 18

ok

Answer 19

Let's call its side-length x.

We know its base length is x. If we can only find the height, then finding the area is simple.

Answer 20

yes

Answer 21

oknow what do I do from here

Answer 22

Now, could you tell me what THIS length is equal to?

Answer 23

the other side

Answer 24

Yes.... of course it is, but what is it equal to?
In terms of x.

Answer 25

1/2

Answer 26

1/2.... are you sure that's it?

Answer 27

not really

Answer 28

Then what ARE you sure of?

Answer 29

that I wanna learn the formula

Answer 30

Right, well, the height neatly divides the base into to equal parts, so this length is just half of the side-length x.

Answer 31

ok that makes sence

Answer 32

What about THIS length?