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
