Question

or two similar triangle, the ratio of two corresponding sides is A1:A2=1:3.
Find the ratio of their areas A1:A2

Answer 1

What do we know about similar triangles?

Answer 2

that they can be proportional?

Answer 3

Exactly. Corresponding sides are proportional. They give us the scaling proportion.

What's the equation for the area of a triangle?

Answer 4

not sure how to answer that because that is the question that they are giving me

Answer 5

We need the equation for an area to see exactly how they relate to one another.

\[A_Triangle = \frac{1}{2} Base \times Height\]

Answer 6

I just need to know ratio if it is 1 to 3

Answer 7

If corresponding sides are proportional, then both the base and the height are also proportional.

In our case, we know that a side of triangle 1 is 3 times the size of a side from triangle 2.

Using that equation, we can relate the area of one triangle to the other.

Answer 8

\[A _{1}:A _{2}=1:3 \]

Answer 9

\[A_1 = \frac{1}{2} B_1 \times H_1\]
\[A_2 = \frac{1}{2} Base_2 \times H_2\]

And we know that:
\[B_1 = 3 \times B_2\]
and
\[H_1 = 3 \times H_2\]

Plugging those into the above equation and solving so that it looks like:
\[A_1 = C \times (\frac{1}{2} B_2 \times H_2)= C \times A_2\]
Shows us what we want to know.

Answer 10

Where C is just some number (the proportionality constant of the areas)

Answer 11

that makes sense

Answer 12

Great!

What do you get for C?

Answer 13

should I plug in any numbers because there is no numbers in this problem

Answer 14

You'll plug in:
\[B_1 = 3B_2, H_1 = 3H_2\]

Since we're told this is true in the problem (A side from triangle 1 is 3 times larger than the corresponding side from triangle 2)

Answer 15

are you a teacher?

Answer 16

I teach physics at a university