If the perimeter of rectangle ABCD is 20 inches, the least value of diagonal AC, in inches, is:

1967 AMC 12 Problem 11

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11.

If the perimeter of rectangle

ABCD

20

inches, the least value of diagonal

AC,

in inches, is:

0

\sqrt{50}

10

\sqrt{200}

none of these

If adjacent sides are

x

and

10-x,

square the diagonal

Complete the square in

x^2+(10-x)^2

Let adjacent sides be

x

and

10-x.

Then

\begin{aligned} AC^2&=x^2+(10-x)^2\\ &=2(x-5)^2+50. \end{aligned}

This is minimized at

x=5,

giving

AC=\sqrt{50}.

Therefore, the correct answer is B.