What is the perimeter of an equilateral triangle if the length of an altitude is 5/sqrt3?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Tony B
Mar 13, 2016

Perimeter is 10

#color(red)("Using ratios is a very powerful tool!")#

Explanation:

Tony B

Let the height of the standardises triangle by # h#
Let the side length of the triangle in the question be #x#

The by ratio of side lengths we have:

#color(blue)(("height of target triangle")/("height of standard triangle")= ("side of target triangle")/("side of standard triangle"))#

#(5/sqrt(3))/h = x/2#

#5/sqrt(3)xx1/h=x/2#

But #h= sqrt(3)# giving

#5/sqrt(3)xx1/sqrt(3) =x/2#

#x=(2xx5)/3#

But this is the length for only one side. There are three sides so:

Perimeter = #(3xx2xx5)/3 = 3/3 xx2xx5=10#

Related questions
See all questions in Problem-Solving Models
Impact of this question
5433 views around the world
You can reuse this answer
Creative Commons License