Answers

1. Answer:

   The width is 7ft and the length is 17 ft

   Step-by-step explanation:

   Let w represent the width of the room and L represents the length of the den.

   Given that:

   caseys den is 10feet longer than it is wide

   Then;

   w + 10 = L —- (1)

   The area of the den = 119 ft²

   Area = w × L

   119 = w × L  —- (2)

   From equation (1);

   let w = L – 10.

   Now we can replace the value of w into equation (2)

   i.e.

   (L – 10) × L = 119

   L² – 10L – 119 = 0

   (L + 7) ( L – 17) = 0

   L + 7 = 0 or L – 17 = 0

   L = – 7 ft  or L = 17 ft

   Recall that:

   w = L – 10

   w = -7 – 10    or    w = 17 – 10

   w = -17         or     w = 7 ft

   The area of the den can now be:

   Area = -17 ft × – 7ft   or       17ft ×  7 ft

   Area = 119 ft²           or        119 ft²

   Since it is ideal to use the positive integer,

   Then the width is 7ft and the length is 17 ft

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