The area of two similar triangles are 24 square cm and 54 square cm. The smaller triangle has a 6-cm side.

Question

How long is the corresponding side of the larger triangle?

 

I would really appreciate if someone knows the answers to this problem.

Answer 1

Sunny,

 

The ratio of the areas of the two similar triangles is equal to the ratio of the squares of two corresponding sides.

 

So:

 

Let x represent the corresponding side in the larger triangle to the smaller side 6.

 

Then:

 

24/54 = 6²/x²

 

Cross multiply to get:

 

24x² = 6² * 54

 

24x² = 36 * 54

 

24x² = 1944

 

x² = 1944/24

 

x² = 81

 

x = sqrt(81) = 9cm (the length of the corresponding side)

 

Hope this helps.