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Four isosceles right triangles were combined as shown above. What is t

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Four isosceles right triangles were combined as shown above. What is t  [#permalink]

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New post 13 Sep 2016, 02:13
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Re: Four isosceles right triangles were combined as shown above. What is t  [#permalink]

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New post 13 Sep 2016, 02:54
Let a be the side of the smallest right triangle.
\sqrt{2a} is the hypotenuse of the smallest triangle and the side of the next bigger triangle
2a is the hypotenuse of the 2nd triangle & the side of the 3rd triangle.
\sqrt{8a} is the hypotenuse of the 3rd triangle and and the side of 4th (biggest) triangle.
4a is the hypotenuse of the biggest triangle.

ratio is 4a/a = 4
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Re: Four isosceles right triangles were combined as shown above. What is t  [#permalink]

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New post 13 Sep 2016, 03:45
If you consider the legs of the smallest isosceles right angled triangle as 1 and work your way through you would get the ratio as 4:1.
legs of smallest triangle will be 1, 1 giving hypotenuse sqrt 2.
apply sqrt 2 as legs of 2nd triangle will give you its hypo as 2.
apply 2 as legs of 3rd triangle will give you its hypo sqrt 8.
apply sqrt 8 as legs of largest triangle to get hypo as 4.
Required ratio is hypo large triangle/ legs of smallest triangle which equals 4/1=4

answer 4:1
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Re: Four isosceles right triangles were combined as shown above. What is t   [#permalink] 13 Sep 2016, 03:45
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Four isosceles right triangles were combined as shown above. What is t

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