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# help plz

0
40
3

A rectangle contains two circles of radius 24 and a circle of radius 16, as shown below.  Each circle is tangent to the other two circles.  Find the area of the rectangle.

Jan 5, 2021

#1
+312
-2

24*2=48

16*2=32

32+48=80

24*4=96

96*80=7680

Jan 5, 2021
#2
+114094
-1

The width is easy = 4 (24)   =  96

The height is a little trickier

Connect the center of the  botton circle with the center of the  circle on the  top right....this distance is  24 + 16  =40

This will form the hypotenuse of a right triangle ....with another leg   =24

And...the height of this triangle  is  sqrt  [ 40^2 - 24^2 ]  = sqrt (1344)  =8sqrt (21)

So....the height of the rectangle is   24 + sqrt (1344)   +  16  =   40 + 8sqrt (21)

The area  =   ( 96 ) ( 40 + 8sqrt (21)  )  ≈   7359.4 units^2

Jan 5, 2021
#3
+824
+3

A rectangle contains two circles of radius 24 and a circle of radius 16, as shown below.  Each circle is tangent to the other two circles.  Find the area of the rectangle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Rectangle length      L = 24 * 4 = 96

Rectangle width       W = sqrt(402 - 242) + 24 + 16 = 72

Rectangle area        A = 96 * 72 = 6912

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There're 3 different answers to this question!?! I understand that there could be more than one solution, but there must be only one correct answer!!!

Jan 6, 2021