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

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.