Another QR Question

[UCF FINatic]

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36.​

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Each of the circles I, II, and III is tangent
to the other two circles. The areas of the
circles are 4π, 9π, and 16π, respectively.
Which represents the length of the
perimeter of the triangle formed by joining​

the centers of three circles?

(see attached picture)

A. 3.0
B. 9.0
C. 14.5
D. 18.0​

E. 29.0

So wouldn't you find the radius of the 3 circles:
Area=(&#960😉r*r
so 2, 3, 4

Then to find the triangles perimeter you add up the 3 sides and get (B.) 9.0

However the answer is apparently (D.) 18.0, I have no clue at all how they got that answer, does anyone here?

 

[jntm46]

If you add the radius of circle I and II, it would give you a length of 5, circle I and III would give you 6, and circle II and II would give you 7, if you add them all up (which is the perimeter) it'll give you the length of 18. So D is correct.

 

[RalphMouth]

Each side is composed of 2 radii, not one radius. For example, center of circle I to center of circle 3 is 2 (radius of smallest circle, I)+4 (radius of largest circle, III) = 6 for that side. II to III is 3+4 = 7. I to II is 2+3 = 5. 6+7+5 = 18

 

[UCF FINatic]

Thanks guys!

I guess I kind of jumped the gun with my answer without actually looking at what the picture was telling me. Hopefully that doesn't happen on the real DAT 😕