SOLUTION: The perimeter of rectangle is 28cm. Find the range of possible values of width of the rectangle if diagonal is less than 10cm

Question 1087255: The perimeter of rectangle is 28cm. Find the range of possible values of width of the rectangle if diagonal is less than 10cm
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let L be the length and W be the width.

Then we have L + W = 14; hence, L = 14-W and the diagonal is

 < 10.

Square both sides:

 < 100  ====>

 < 100  ====>

 < 0  ====>

 < 0  ====>

the roots of the quadratic equation  = 0  are

 =  =  =   ====>

1)   = 8;   2)   = 6.


The width is between 6 and 7   (I accept that the width is the smaller dimension of the rectangle).


Answer.  At given conditions, the range of possible values of the width of a rectangle is the interval (6,7) 
         (accepting that the width is the smaller of the two dimensions of a rectangle).

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