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.
+128474 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
+1639 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.
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Rectangle length L = 24 * 4 = 96
Rectangle width W = sqrt(402 - 242) + 24 + 16 = 72
Rectangle area A = 96 * 72 = 6912 
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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!!! 
