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Re: Figures X and Y above show how eight identical triangular pieces of ca
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09 Oct 2016, 17:55
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
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13 Oct 2016, 01:26
jonmarrow wrote:
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 \(2\sqrt{2} :3\).
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Re: Figures X and Y above show how eight identical triangular pieces of ca
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14 Mar 2017, 03:18
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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?
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 \(= 4*\sqrt{2} : 6 = 2\sqrt{2} : 3\)
Answer (C)
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Re: Figures X and Y above show how eight identical triangular pieces of ca
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16 Aug 2017, 11:51
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
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Updated on: 16 Apr 2018, 11:37
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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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21 Sep 2017, 21:44
This is a good question Take √2 is a length of one side of the square Then we have perimeter of the square = 4√2 perimeter of the rectange is 6 ten ration = 4√2 : 6 = 2√2: 3
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18 Dec 2017, 04:44
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?