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47% (02:09) correct
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The figure above shows a rectangle and five circles. Each circle is tangent to the other circles and to the sides of the rectangle that it touches. If the diameter of each circle is 4, what is the area of the rectangle?
A. 24 + 12√2
B. 24 + 12√3
C. 48 + 24√2
D. 48 + 24√3
E. 96
Attachment:
2022-11-25_19-01-25.png [ 28.38 KiB | Viewed 3022 times ]
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Bunuel
The length of the rectangle is the sum of the diameter of the three circles and is equal to 12 units.
To find the breadth, we can join the midpoints of the three triangles and shown to obtain an equilateral triangle PQR.
Each angle in PQR is 60. Drop a perpendicular from P to QR at point X.
In \(\triangle PQX\)
- \(\angle PQR = 60^{\circ}\)
- \(\angle QPX = 30^{\circ}\)
- \(\angle PXQ = 90^{\circ}\)
- PQ = 4
- PX = \(2\sqrt{3}\) (using 30 - 60 - 90)
Breadth of the rectangle = PM + PX + XN = \(2 + 2\sqrt{3} + 2 = 4 + 2\sqrt{3}\)
Area = \(12 * 4 + 2\sqrt{3} = 48 + 24\sqrt{3}\)
Option D
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
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