## rtraylor3 3 years ago Find the measure please, I got 3 but it's wrong?

1. rtraylor3

2. eseidl

find the measure of what?

3. eseidl

D?

4. rtraylor3

Sorry the area of triangle DEF

5. eseidl

ok, so A=12 is the area of the first triangle

6. rtraylor3

Yes. I went by the side of the first and second. The first was 4 and the second was 1 so I thought that the first triangle was 4 times greater than the second. 12/4=3

7. eseidl

each side of the triangle on the right is scaled down by a factor of 1/4.

8. rtraylor3

Correct...

9. eseidl

Area of a triangle is base*height/2 so,$\frac{\left| AC \right|4*\sin A}{2}=12$for the triangle on the left. The triangle on the right is:$\frac{\left| DF \right|1*\sin D}{2}=?$Sow the sides AC and DF are related. DF=(1/4)AC and the angles A and D (and therefore their sines) are equal. so, we can write the second equation above as:$\frac{(1/4)\left| AC \right|1*\sin A}{2}=?$comparing this with the first equation, we see that 2AC*sinA=12 and (1/8)AC*sinA=?. Now we see that the second equation is 1/16 of the first one. So the area of the second triangle must be 12/16=3/4

10. eseidl

So, in summary, if one side of a triangle is scaled by a factor of x, then the area of the second triangle is x^2*area of the first.

11. eseidl

where x=1/4 in this example.

12. rtraylor3

Thanks so much!! I got it now!

13. eseidl

no prob :)

14. rtraylor3

New fan= me(:

15. eseidl

and if you are scaling volumes, it is the same type of argument. Only now you use x^3 instead of x^2 because there is an extra dimension.