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Math Expert V
Joined: 02 Sep 2009
Posts: 60517
Four isosceles right triangles were combined as shown above. What is t  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 82% (01:38) correct 18% (03:02) wrong based on 50 sessions

### HideShow timer Statistics Four isosceles right triangles were combined as shown above. What is the ratio of the hypotenuse of the largest triangle to the leg of the smallest triangle?

A. 2√2
B. 4
C. 3√2
D. 2+2√2
E. 4√2

Attachment: T6032.png [ 2.72 KiB | Viewed 1168 times ]

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

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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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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 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  