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

In the figure below, the triangles are similar. Find the ratio of their areas from-example-1
User Jason Silver
by
2.5k points

1 Answer

17 votes
17 votes
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
User Regev Avraham
by
3.1k points