Question

If a 2.5 g sample of gold is hammered into an equilateral triangle that is .28mm thick, how long are the sides?

Answer 1

Okay, let's first determine the volume of the triangle.

Volume of the triangle
= Mass of the triangle/Density of gold
= 2.5/19.3
= 0.129533678cm³

1mm= 0.1cm
0.28mm= (0.1)(0.28)
= 0.028cm

Volume of a solid
= (area of its cross section)(thickness)

Area of the triangle
= Volume/thickness
= 0.129533678/0.028
= 4.626202813cm²

Answer 2

I think I know how to do it. I need to find the height or something right? :/

Answer 3

Oh ok

Answer 4

that works too

Answer 5

wait where did you get the 19.3 from?

Answer 6

Multiplying them

Answer 7

Now, in an equilateral triangle, each angle is 60°. The area of a triangle is determined using the formula (1/2)absin60°, where a and b are the lengths of two of its sides. Since a=b in the case of the equilateral triangle, its area= (1/2)L²sin60°, where L is the length of each of its sides.

(1/2)L²sin60°= 4.626202813
L²= (2)(4.626202813)/sin60°
L²= 10.68375776
L= |√10.68375776|
= 3.268601805cm
= 3.3cm correct to 2 significant figures

Answer 8

Does that answer your question? :)

Answer 9

Somewhat....

Answer 10

How could I figure out the lenght of the sides though?

Answer 11

Now I'm just confused.. :/

Answer 12

The answer is = 3.268601805cm

Answer 13

Really? For all three sides?

Answer 14

For 2

Answer 15

actually

Answer 16

Oh yeah beacuse it is an equilateral triangle which means all sides are the same

Answer 17

L²= (2)(4.626202813)/sin60°
L²= 10.68375776
L= |√10.68375776|

Answer 18

Those are the sides

Answer 19

So does it make sense now?

Answer 20

and yes it is because its equilateral triangle :)

Answer 21

Yeah! So the two answers are the 10.6 and 3.26?

Answer 22

All three sides are 10.6 :D GoodJob

Answer 23

Thank you!

Answer 24

You're welcome :)