If the area of an equilateral triangle is 4 times...

[Alexander]

Hi -


"If the area of equilateral triangle ABC is 4 times that of equilateral triangle PQR, then each side of ABC is how many times the corresponding side of PQR?"

I think the explanation is prolix ( points for studying vocab ?! ) - can you explain it in a different manner? I tried plugging numbers in for this since I knew the formula but couldn't get it in <2 min.

Thanks,
Alexander

[tommywallach]

The area of any equilateral triangle can be expressed as:

1/2 * x rt. 3 * 2x (where the base of the triangle is 2x and the height is x rt. 3, because any equilateral divides into two 30-60-90s).

So what would we need to do to x to make the result 4 times bigger? Well, if we double x, the area will be 4 times bigger, (because there are two x's in the equation).

Tada!

-t

P.S. To plug in here just say:

1/2 * x rt. 3 * 2x = 20 rt. 3 (I made up this area. I put the rt. 3 on it on purpose, so it will cancel out)

1/2 * x rt. 3 * 2x = 80 rt. 3 (4 times as much as before)

Then solve both for x.