Question

A piece of wire 6x cm long is bent into an equilateral triangle. For which values of x will the area be numerically less than the perimeter?

Answer 1

@zzr0ck3r Could you help me wit this problem please?

Answer 2

If a wire that's 6cm long is bent into an equilateral triangle, what is the length of each side?

Answer 3

6x cm long*

Answer 4

2 cm?

Answer 5

6cm/ 3 sides= 2 cm

Answer 6

Correct, but we also have that x, so it would be 2x cm for each side. Now, we have an equilateral triangle with 2x cm on each side, how would we find the area?

Answer 7

A=1/2bh so A=1/2(2)(2)??

Answer 8

not sure about height though

Answer 9

The height of an equilateral triangle is
\[\frac{ x \sqrt{3} }{2 }\]
where x is the length of one side.

Answer 10

would the base be 2 though?

Answer 11

Yes, the side lengths are 2x, so the base would be 2x.

Answer 12

now just solve for x correct?

Answer 13

What did you get for the area of the triangle? We know that the perimeter is 6x, now we just need to find the area so we can set up an inequality to figure out what values of x allow the perimeter to be greater than the area.

Answer 14

i don't what the Area is?

Answer 15

If you know the base is 2x and the is height formula is posted above, just do 1/2bh to find it.

Answer 16

but what about the root3?