## 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?

Question

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?

in progress 0
3 years 2021-08-14T16:00:10+00:00 1 Answers 7 views 0

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