# Ratio of the areas of two similar triangles

• Jan 30th 2010, 03:43 PM
FHS93
Ratio of the areas of two similar triangles
The ratio of the areas of two similar triangles is 16:9. What is the ratio of the lengths of corresponding sides? Please show your work here.
• Jan 30th 2010, 04:16 PM
jasonlewiz
Quote:

Originally Posted by FHS93
The ratio of the areas of two similar triangles is 16:9. What is the ratio of the lengths of corresponding sides? Please show your work here.

Area of triangle 1 = 16
Area of triangle 2 = 9

Since area is the only one given I suppose that the triangle is an equilateral

get the sides of T1

16x4=64/square root of 3=36.95 then square the answer give you 6.08

get the sides of T2

9x4=36/square root of 3=20.78 then square the answer give you 4.56

Now get the ration T1:T2

6:5 ^^
• Jan 30th 2010, 06:32 PM
mr fantastic
Quote:

Originally Posted by FHS93
The ratio of the areas of two similar triangles is 16:9. What is the ratio of the lengths of corresponding sides? Please show your work here.

You're expected to know and apply that if \$\displaystyle L_1 = k L_2\$ then \$\displaystyle A_1 = k^2 A_2\$.