Question

Help!!

Use the diagram of the equilateral triangle shown below to answer the following questions. Show the work that leads to your answers. a. What is the perimeter of the triangle? b. What is the height, ℎ mm, of the equilateral triangle? Write an exact answer using a square root and an approximate answer rounded to the tenths place.

Answer 1

Perimeter is 12mm, height is
`2\sqrt3`mm in simplest radical form, and 3.5mm in approximate decimal form.

Explanation:

The perimeter is easy; since it's an equilateral triangle, all sides are the same length of 4, so you can just do 3*4 (3 sides, 4mm each) to get a perimeter of 12.

For the height, you can see that it forms two right triangles, each with a given base of 2 and a hypotenuse of 4. We can apply the pythagorean theorem (
`a^2+b^2=c^2`) here to find the missing leg length of the smaller right triangles, which is equal to the big triangle's height.

I've enclosed an attachment for that.

Hope this helps!