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ABCD is a square with AB=10. What is the perimeter of the sh

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by Max@Math Revolution » Thu Jul 25, 2019 12:13 am

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[GMAT math practice question]

ABCD is a square with AB=10. What is the perimeter of the shaded area?

Image

A. 10Ï€/3 +10
B. 5Ï€/3 +10
C. 5Ï€/6 +10
D. 5Ï€/3 +5
E. 5Ï€/6 +5
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by GMATGuruNY » Thu Jul 25, 2019 2:22 am
The prompt should indicate that ABC and BCD are quarter-circles.
Max@Math Revolution wrote:[GMAT math practice question]

ABCD is a square with AB=10. What is the perimeter of the shaded area?

Image

A. 10Ï€/3 +10
B. 5Ï€/3 +10
C. 5Ï€/6 +10
D. 5Ï€/3 +5
E. 5Ï€/6 +5
Perimeter of shaded region = AD + (AP+DP) = 10 + (more than 10)
Only A is viable:
(10Ï€)/3 + 10 = more than 10 + 10

The correct answer is A.
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by Max@Math Revolution » Sun Jul 28, 2019 4:56 pm
=>

Image

Since triangle PBC is equilateral, angle ABP has measure 30° and the length of arc AP is 2π*10*(30/360) = (5/3) π.
Thus, the perimeter of the shaded area is (5/3) π *2 + 10 = (10/3) π + 10.


Therefore, A is the answer.
Answer: A
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