Question

I don't understand, please help!
If the ratio of the lengths of corresponding sides of two similar triangles is 2 : 3, and the area of the smaller triangle is 36 in.2, what is the area of the larger triangle?
A. 24 in.2
B. 54 in.2
C. 81 in.2
D. 90 in.2

I can do everything else in this unit but for some reason I don't understand how to do this, any tipz would help :)

Answer 1

@ganeshie8
@ParthKohli
Can you guys help?

Answer 2

Since the shape is 2D we need to use the square of the linear scale factor to scale the area. (i.e. The lines are 1D and thes hape is 2D). (If it was a 3D shape it would be the cube etc.)

So to start: what is your linear scale factor in simplest form?

Answer 3

2:3. I remember them talking about this, and saying to square them both (4:9) but I don't know what to do after that.

Answer 4

Right, you can square them first and then reduce to simpler terms or you can reduce first and then square. The order doesn't really matter. It's whatever you prefer.

Answer 5

But if I square 2:3 it comes out 4:9, then I do 4/9 and it's 0.444444 repeating.

Answer 6

That's true, but you can also go the other way: (ie. 9/4) If you think about it, were going from a smaller shape to a bigger shape, so would it make sense to have a number bigger or smaller than 1?

Answer 7

I guess I could do 2:3, then square it which would be 4:9, then set up an equal like this:
\[\frac{ 4 }{ 9 } = \frac{ 36 }{ x }\]
and then I could just solve for x, would that work?

Answer 8

If I do it like that, then x = 81, which is one of the answers, so I think I just guessed the right way to solve this lol.

Answer 9

Yes, that's a very could way to do it. I was going to walk you through it step by step but using the ratios is much faster. Good job.

Answer 10

Thanks! Here's a medal.

Answer 11

The other way that you could do it is: \[\frac{3}{2}=1.5\]\[1.5^{2}=2.25\]\[36 \times 2.25 =81\]