Question

In the figure below, the triangles are similar. Find the ratio of their areas from larger to smaller.

Answer 1

Area of larger triangle is A1
21:14=x:8
x=21•8/14
x=168/14
x=12
x=base of triangle
A2=h•b/2
21^2=6^2+h^2
441=36+h^2
h^2=441-36
h^2=405
h= √405
h=20.12

A1=12•20.12/2
A1=6•20.12
A1=120.72


Area of smallest triangle is A2
A2=b•h/2
h=?
14^2=4^2+h^2
196=16+h^2
h^2=196-16
h^2=180
h= √180
h=13.42
A2=8•13.42/2
A2=4•13.42
A2=53.68

Ratio 120.72:53.68
Ratio=2.25