Posted by **deana** on Wednesday, January 25, 2012 at 3:55pm.

51. The ﬁgure below illustrates an isosceles right

triangle with legs of length 1, along with onefourth of a circle centered at the right-angle

vertex of the triangle. Using the result that

the shortest path between two points is a line

segment, explain why this ﬁgure shows that

2(squareroot of 2) <2

- math -
**Reiny**, Wednesday, January 25, 2012 at 5:10pm
I see this is the second time you posted this.

Of course you realize that we can't see any diagram, but I think I can draw it from your description

First of all, you must have a typo.

Did you mean 2√2 < π ??

Since your statement of2√2 < 2 is false, (2√2 = appr. 2.8)

In the triangle let the hypotenuse be h

h^2 = 1^2 + 1^2 = 2

h = √2

the arc is (1/4)(2π) = π/2

then because of the straight between two points is always less than a curve between the same two points,

√2 < π/2

multiply by 2

**2√2 < π **

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