casey's den is 10feet longer than it is wide. If the den's area is 119 square feet, what are the dimensions of the room?

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

no this is a nonlinear negative