SOLUTION: The perimeter of a rectangle is 32cm. What is the shortest possible diagonal of the rectangle?
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Question 1012985: The perimeter of a rectangle is 32cm. What is the shortest possible diagonal of the rectangle?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sides are x and 16-x
They add to 16 which is half the perimeter.
square them to x^2 and (16-x)^2, and that equals D^2, where D is the diagonal.
x^2+256-32x+x^2=D^2
D^2=2x^2-32x+256
The minimum is the vertex and x=-b/2a at the vertex. That is 32/4=8
The diagonal is shortest when the rectangle is a square, with sides 8. The diagonal length squared is 128, so the diagonal is 8 sqrt(2), from a 45-45-90 right triangle.
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