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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

1 Answer

3 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 Glen Little
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