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Figures X and Y above (OG2016)

This topic has 2 expert replies and 1 member reply
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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Figures X and Y above (OG2016)

Post Fri May 06, 2016 12:37 pm
ttp://postimg.org/image/xnwmp2jup/" target="_blank">

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?
A) 2 : 3
B) sqrt2 : 2
C) 2sqrt2 : 3
D) 1 : 1
E) sqrt2 : 1

OA: C

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Post Mon Sep 11, 2017 12:23 pm
boomgoesthegmat wrote:
ttp://postimg.org/image/xnwmp2jup/" target="_blank">

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?
A) 2 : 3
B) √2 : 2
C) 2√2 : 3
D) 1 : 1
E) √2 : 1

OA: C
Let's start by gathering more information about these eight identical triangles.
First notice that we have 4 equal angles meeting at a single point.
ttps://postimages.org/" target="_blank">

So, each angle must be 90°
ttps://postimages.org/" target="_blank">

Now examine the red triangle below.
ttps://postimages.org/" target="_blank">

The red triangle is an isosceles triangle since all 4 sides of a square are equal.
The two equal angles must add to 90°
So, each angle must be 45°
ttps://postimages.org/" target="_blank">

Using similar logic, we can conclude that all of the eight triangles are 45-45-90 special right triangles.
ttps://postimages.org/" target="_blank">

Now let's examine what happens if we examine one particular 45-45-90 special right triangle, which has sides of length 1, 1 and √2
ttps://postimages.org/" target="_blank">

Use those lengths for all eight identical triangles in the 2 diagrams we get the following:
ttps://postimg.org/image/re4jt2p9h/" target="_blank">

At this point, we can calculate the perimeters.
Perimeter of X = √2 + √2 + √2 + √2 = 4√2
Perimeter of Y = 1 + 1 + 1 + 1 + 1 + 1 = 6

So, perimeter of X : perimeter of Y = 4√2 : 6
Divide both sides by 2 to get the equivalent ratio 2√2 : 3

Answer: C

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Post Thu May 12, 2016 12:23 am
Suppose each side of the square has length 1. Its perimeter = 4.

The side of the square is a diagonal to the midpoint of y. That triangle has angles of 45°, so each leg has length 1/√2, or √2/2.

The perimeter of that rectangle is 6 * √2/2, or 3√2.

The ratio is thus 4 : 3√2. Dividing both parts of the ratio by √2 gives 2√2 : 3, or C.

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Post Mon Sep 11, 2017 12:23 pm
boomgoesthegmat wrote:
ttp://postimg.org/image/xnwmp2jup/" target="_blank">

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?
A) 2 : 3
B) √2 : 2
C) 2√2 : 3
D) 1 : 1
E) √2 : 1

OA: C
Let's start by gathering more information about these eight identical triangles.
First notice that we have 4 equal angles meeting at a single point.
ttps://postimages.org/" target="_blank">

So, each angle must be 90°
ttps://postimages.org/" target="_blank">

Now examine the red triangle below.
ttps://postimages.org/" target="_blank">

The red triangle is an isosceles triangle since all 4 sides of a square are equal.
The two equal angles must add to 90°
So, each angle must be 45°
ttps://postimages.org/" target="_blank">

Using similar logic, we can conclude that all of the eight triangles are 45-45-90 special right triangles.
ttps://postimages.org/" target="_blank">

Now let's examine what happens if we examine one particular 45-45-90 special right triangle, which has sides of length 1, 1 and √2
ttps://postimages.org/" target="_blank">

Use those lengths for all eight identical triangles in the 2 diagrams we get the following:
ttps://postimg.org/image/re4jt2p9h/" target="_blank">

At this point, we can calculate the perimeters.
Perimeter of X = √2 + √2 + √2 + √2 = 4√2
Perimeter of Y = 1 + 1 + 1 + 1 + 1 + 1 = 6

So, perimeter of X : perimeter of Y = 4√2 : 6
Divide both sides by 2 to get the equivalent ratio 2√2 : 3

Answer: C

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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