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# The figure above is formed by connecting perpendicular line segments

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Math Expert
Joined: 02 Sep 2009
Posts: 49300
The figure above is formed by connecting perpendicular line segments  [#permalink]

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09 Nov 2017, 23:26
00:00

Difficulty:

35% (medium)

Question Stats:

64% (02:06) correct 36% (02:11) wrong based on 28 sessions

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The figure above is formed by connecting perpendicular line segments that have lengths as shown. What is the length of the dashed line segment?

(A) 5
(B) 2√7
(C) 4√2
(D) √34
(E) √41

Attachment:

2017-11-07_0942.png [ 6.03 KiB | Viewed 658 times ]

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Joined: 22 May 2017
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GMAT 1: 580 Q41 V29
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Re: The figure above is formed by connecting perpendicular line segments  [#permalink]

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11 Nov 2017, 06:01
Bunuel wrote:

The figure above is formed by connecting perpendicular line segments that have lengths as shown. What is the length of the dashed line segment?

(A) 5
(B) 2√7
(C) 4√2
(D) √34
(E) √41

Attachment:
2017-11-07_0942.png

calculate the diagonal of the triangle formed by figure. then you will get answer 2 square root 4.

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Joined: 22 May 2016
Posts: 1978
The figure above is formed by connecting perpendicular line segments  [#permalink]

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11 Nov 2017, 11:15
1
Bunuel wrote:

The figure above is formed by connecting perpendicular line segments that have lengths as shown. What is the length of the dashed line segment?

(A) 5
(B) 2√7
(C) 4√2
(D) √34
(E) √41

Attachment:
The attachment 2017-11-07_0942.png is no longer available

Attachment:

ttt.png [ 23.74 KiB | Viewed 403 times ]

See attached figure.
Connected perpendicular lines = all lines are parallel such that the distance between the two at any given point is the same.
To find lengths of sides of what turns out to be an isosceles right triangle

1. Extend right side of figure down - gray dotted line: whole side length = 7 (parallel to other side whose length = 7)
Part of that line = one side of a right triangle whose hypotenuse is the black dotted line
From the right side, extend a line horizontally until it meets the hypotenuse, to form the other side of the triangle.

See small labeled triangle.

2. Length of BC = (9 - 7) = 2

3. Length of AB = (5 - 3) = 2

4. Length of CD = (3 - 1) = 2

5. Length of DE = (7 -5) = 2

Each side of the right triangle = (2 + 2) = 4

Isosceles right triangles have side lengths in ratio $$x: x: x\sqrt{2}$$
$$x = 4$$
$$x\sqrt{2} = 4\sqrt{2}$$= hypotenuse = black dashed line

OR

$$4^2 + 4^2 = (hypotenuse)^2$$
$$(16 + 16) = 32 = h^2$$
$$h = \sqrt{32}$$
$$h = \sqrt{16 * 2}= 4\sqrt{2}$$ = black dashed line

black dashed line = $$4\sqrt{2}$$

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The figure above is formed by connecting perpendicular line segments &nbs [#permalink] 11 Nov 2017, 11:15
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