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The perimeter of quadrilateral ABCD

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The perimeter of quadrilateral ABCD [#permalink] New post   07 Dec 2022, 03:31
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Quantity A
Quantity B
The perimeter of quadrilateral ABCD
The area of the shaded region



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
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B
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B
rainer85
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Re: The perimeter of quadrilateral ABCD [#permalink] New post   07 Dec 2022, 20:07
The diamond generates two different triangles, each with a base of 10 and a height of 12.
Area of a triangle = .5 * 10 * 12 = 60 + 60 (adding 60 since there are two triangles with this area) = 120 = QB

QA: use the Pythagorean theorem, the diamond generates four triangles, each with legs that have lengths of 5 and 12 and thus a hypotenuse of 13 (5^2 + 12^2 = 13^2). 13 * 4 = 52

QB is larger
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Re: The perimeter of quadrilateral ABCD [#permalink] New post   11 Dec 2022, 04:00
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OE


The axes split the quadrilateral into four equal 5-12-13 right triangles. So the perimeter is 4(13) = 52, and the area of each of the 4 triangles is 30 for a total area of 120. Quantity B is therefore greater.
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Re: The perimeter of quadrilateral ABCD [#permalink]
11 Dec 2022, 04:00
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