Math CentralQuandaries & Queries



Question from Chandler, a student:

I need help with finding the scale factors of triangles I asked a question a while ago about square roots and I thoroughly appreciate the answer. anyway I am rather confused about finding the area of a triangle they give me the area of the larger triangle it is 25 units but I can't figure out how to find the area of the smaller triangle the scale is 3:5 please help me ASAP. Thanks so much I really appreciate it oh the triangles are similar

We have two responses for you.

Hi Chandler,

What makes thus problem solvable is your final comment "the triangles are similar".

Suppose that you have two similar triangles the large triangle has base of length B and height H and the smaller triangle has base of length b and height h. Since the triangles are similar

B/b = H/h

I am going to call this number s, the scale factor so

B/b = H/h = s

and hence

B = s times b and H = s times h

The area of the small triangle is a = 1/2 bh and the area of the large triangle ia A = 1/2 BH. Thus

A = 1/2 BH = 1/2 s b s h = 1/2 s2 bh = s2 a

You know A is 25 square units and hence to find a you only need to find s. You are told that the scale is 5:3 so

B/b = H/h = 5/3

and thus s = 5/3.



Hi Chandler.

Scales are normally given on a linear basis. That means a line that is 5 units on large triangle is 3 units on the small triangle. Area scale is the square of the linear scale, because area is measured in (linear units)2.

So your area scaling factor is (3/5)2. It works similarly for volume.

Hope this helps,
Stephen La Rocque.

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