Geometry

[Gmatasap]

In the figure above, ABCD is a square, and the two diagonal lines divide into three regions of equal area. If AB =3, what is the approximate length of w, the perpendicular distance between the two diagonal lines?
A. 0.8
B. 1.2
C. 1.4
D. 1.8
E. 2.1

Source Manhattan Prep Test
OA A

[GMATGuruNY]

In the figure above, ABCD is a square, and the two diagonal lines divide it into three regions of equal area. If AB = 3, what is the length of w, the perpendicular distance between the two diagonal lines?

A) 3√2 - 2√3
B) 3√2 - √6
C) √2
D)
E) 2√3 - √6

The area of square ABCD = 3² = 9.

Since the square is divided into 3 equal regions, the area of triangle DWY = 3.
Thus:
(1/2)(DY)(WD) = 3.
Since triangle DWY is isosceles, DY=WD.
Thus:
(1/2)(WD)(WD) = 3
WD² = 6
WD = √6.

Since AD = 3 and WD = √6, AW = 3 - √6.
Triangle AXW is a 45-45-90 triangle.
(Don't worry about a proof. It should be clear from the figure that AXW is an isosceles right triangle.)
Since the sides in triangle AXW are proportioned 1:1:√2, we get:
WX = (3 - √6)√2 = 3√2 - √12 = 3√2 - 2√3.

The correct answer is A.

[Gmatasap]

Thank you for the answer. I have a stupid question. How often do we get the options in values as I got in my question. Are the answers in roots more popular or the do we equally often get the answers in points system

[Brent@GMATPrepNow]

Hi Gmatasap,

You're more likely to see answer choices as exact root values (e.g., √3) than as approximate values (e.g., 1.7)
That said, you need to be proficient at both.

Cheers,
Brent

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