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In the diagram above, each circle is in contact two other circles and at least one side of the rectangle. The radii are perpendicular to the sides of the rectangle as shown. Find the area of the rectangle

 

 Jul 2, 2020
 #1
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Area = 6912.

 Jul 2, 2020
 #2
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Let  A  =  center of the top-left circle.

Let  B  =  center of the top-right circle.

Let  C  =  center of the bottom circle.

 

Draw AB; label the point of tangency of the two circle  X.

Draw AC; its length is 24 + 16  =  40.

AX  =  24.

Use the Pythagorean Theorem to find XC:  XC2 + XA2  =  AB2     --->     XC2 + 242  =  402

Solving:  XC  =  32.

 

The width of the rectangle is  24 + 24 + 24 + 24  =  96

The height of the rectangle is:  24 + 32 + 16  =  72

 

From these two dimensions, you can find the area.

 Jul 2, 2020
 #3
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This question is too easy. Try this one: find the area of a rectangle if its area is 10 times the area of a smaller circle.

 Jul 3, 2020

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