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Re: Figures X and Y above show how eight identical triangular pieces of ca [#permalink]

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09 Oct 2016, 18:55

for square, i dont understand how the side is calculated to be sqaure root 2? should not that be the amount of the DIAGONAL and not the 4 sides? side = 1. perimeter = 4*1 = 4

for square, i dont understand how the side is calculated to be sqaure root 2? should not that be the amount of the DIAGONAL and not the 4 sides? side = 1. perimeter = 4*1 = 4

Which solution are you referring to?

We have right isosceles triangles.

If we consider the hypotenuse of the triangle to be 1 (notice that the hypotenuse of the triangle = the side of the square), then the legs of the triangle will be \(\frac{1}{\sqrt{2}}\) (notice that a leg of the triangle = the width of the rectangle).

If we consider the legs of the triangle to be 1 (notice that the a leg of the triangle = the width of the rectangle), then the hypotenuse will be \(\sqrt{2}\) (notice that the hypotenuse of the triangle = the side of the square).

In any of the cases the ration of the perimeters comes to be \(2\sqrt{2} :3\).
_________________

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?

My Query: I am getting A as the answer since I am trying to relate side of square as (a) and perimeter as 4a. Where am I going wrong

You are right about side of square a has perimeter 4a.

But note how the sides of each triangular piece are related. The two legs, which will be identical in all triangles are say of length L each. The triangles are right angled so the hypotenuse will be \(\sqrt{2}L\).

The square is made up of 4 hypotenuse. The perimeter will be \(4*\sqrt{2}L\). The longer sides of the rectangle are made up of 2 legs each and the shorter sides are made up of L each. Perimeter = 2*2L + 2L = 6L

The ratio of perimeters \(= 4*\sqrt{2} : 6 = 2\sqrt{2} : 3\)

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: Figures X and Y above show how eight identical triangular pieces of ca [#permalink]

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16 Aug 2017, 12:51

Bunuel wrote:

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?

Figures X and Y above show how eight identical triangular pieces of ca [#permalink]

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11 Sep 2017, 13:25

Top Contributor

Bunuel wrote:

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?

ASIDE: Please note that I didn't have to use those specific lengths (1, 1 and √2) for each of the 45-45-90 triangles. I could have used ANY measurements that could be found in a 45-45-90 triangle. For example, I could have used 5, 5 and 5√2, and those measurements still would have yielded the same ratio (after some simplifying)

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