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):
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).
