Question

Assume the original triangle in stage 1 had a side length of one.a) Write a formula that would give the length of a side of one of the triangles at the nth stage.If we look at the stage 1 triangle, we can find it's area by multiplying one-half times the length of it's base times the length of it's height. Assume again that it has a side length of one.b) Find the height of the triangle in stage 1.c) Find the area of the triangle in stage 1.

Answer 1

Part a) length L , of n triangle

Then ,every blue triangle is divided in 4

and, every white triangle, stays similar

for example

at stage 3 , there are 9 blue triangles

3 white triangles

and 1 big white triangle

Here base-length is 1/4

Then answer is

for nth triangle length = 1/2^(n-1)

Part b) Height of triangle = √(1 - 1/2^2) = (use right angle rule a^2+b^2=c^2)

. = √3/2

Part c) Area of triangle,in stage 1

Area = Base x Height/2= 1• (1/2)•√3 /2 = √3/4