Four isosceles right triangles were combined as shown above. What is the ratio of the hypotenuse...

[BTGmoderatorLU]

Source: Economist GMAT

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. \(2\sqrt{2}\)
B. \(4\)
C. \(3\sqrt{2}\)
D. \(2+2\sqrt{2}\)
E. \(4\sqrt{2}\)

The OA is B

[swerve]

Source: Economist GMAT
T6032.png
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. \(2\sqrt{2}\)
B. \(4\)
C. \(3\sqrt{2}\)
D. \(2+2\sqrt{2}\)
E. \(4\sqrt{2}\)

The OA is B

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 and the side of the 3rd triangle.

\(\sqrt{8a}\) is the hypotenuse of the 3rd triangle and the side of the 4th (biggest) triangle.

\(4a\) is the hypotenuse of the biggest triangle.

ratio is \(\dfrac{4a}{a} = 4\)