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

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https://gmatclub.com/forum/download/file.php?id=60618 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 Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 1.png

Showmeyaa · Answer

I have attached the image that contains detailed solution for the above mentioned problem.

sumitkrocks · Answer

Total 4 triangles-
Smallest isosceles right angle triangle leg length=1 Hypotenuse = \sqrt{2} 
For 2nd triangle leg= \sqrt{2}  Hypotenuse = \sqrt{4} 
for 3rd leg= \sqrt{4}  Hypotenuse = \sqrt{8} 
for 4th leg= \sqrt{8}  Hypotenuse = \sqrt{16}  =4

Ratio of Hypotenuse Of 4th/Leg of first=4/1=4

B is the right answer in my opinion

asishron29181 · Answer

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?

In a 45-45-90 triangle, ratio of sides are x-x-√2x

Let the length of smallest side = x and since it is right isosceles triangle , longest side becomes √2 x
Now similarly for the second isosceles triangle longest side becomes 2x
for the 3rd longest side becomes 2 √2 x
for the fourth, longest side = 4x

Ratio of longest side to shortest side = 4
 IMO B

Kyala1Jameson · Answer

imo  B

All are isosceles right angle triangle
Smallest isosceles right angle triangle leg length= x  
Hypotenuse = \sqrt{2}x

For 2nd triangle leg= \sqrt{2}x  
 Hypotenuse = \sqrt{4}x

for 3rd tringle leg= \sqrt{4}x  
 Hypotenuse = \sqrt{8}x

for Biggest triangle leg= \sqrt{8}x  
 Hypotenuse = \sqrt{16}x  =4

Ratio of Hypotenuse Of 4th/Leg of first= \frac{4x}{x} =4

TarunKumar1234 · Answer

side of smallest triangle = x
then, hypotenuse = √2 x = side of another triangle

then hypotenuse of next triangle = √(√2 ^2 + √2^2) x= 2x = side of next triangle

then hypotenuse of next triangle = √(2 ^2 + 2^2) x= 2√2 x = side of next triangle
then hypotenuse of next triangle = √[(2√2) ^2 + (2√2)^2] x= 4 x
So, required ratio = 4x/x = 4

So, I think B.

winterschool · Answer

let,  a  be the two edges of the smallest triangle; so, hypotenuse,  h1 = a\sqrt{2}

h1  will be two edges of next triangle; so  h2 = 4a^2 = 2a

similarly,  h3 = a2\sqrt{2}  and  h4 = 4a

h4  is the hypotenuse of largest triangle
so,  h4/a = 4a/a = 4

Answer B

ScottTargetTestPrep · Answer

Solution:
 
If we let the leg of the smallest triangle be 1, then the leg of the second smallest triangle is √2 (since it’s the hypotenuse of the smallest triangle). Next, the leg of the second largest triangle is √2 x √2 = 2 (since it’s the hypotenuse of the second smallest triangle). Finally, the leg of the largest triangle is 2√2 (since it’s the hypotenuse of the second largest triangle), and the hypotenuse of the largest triangle is 2√2 x √2 = 4. Therefore, the ratio of the hypotenuse of the largest triangle to the leg of the smallest triangle is 4/1 = 4.

Answer: B

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

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

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