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If quadrilateral ABCD, pictured above, has a perimeter of 64

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by Vincen » Sat Nov 30, 2019 7:46 am
Image

If quadrilateral ABCD, pictured above, has a perimeter of 64, what is the length of line segment AD?

(1) The length of line segment AD is equal to the length of line segment BC

(2) Line segment AD is perpendicular to line segment BC

[spoiler]OA=B[/spoiler]

Source: Veritas Prep
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Source: — Data Sufficiency |
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by nitink » Tue Dec 03, 2019 12:06 pm
from 1, the length of diagonal is same. So the quadrilateral is either square or rectangle. But we cant figure out what is it. So, not sufficient.

From 2, diagonals are perpendicular to each other. So, the quadrilateral is either square or rhombus.

So, side = 64/4= 16

In square or rhombus, diagonals bisect each other and are perpendicular to each other.

Using Pythagoras Theorem, we can find out the length of the diagonal.

Hence sufficient.

Hence B
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