Janas' den is 4 feet longer than it is wide. If the​ den's area is 221 square​ feet, what are the dimensions of the​ room?

Question

Janas' den is 4 feet longer than it is wide. If the​ den's area is 221 square​ feet, what are the dimensions of the​ room?

Answer 1

Let x be the width of the den, this means x * (x+4)=221

we can solve this to ^{x^2}+4x =221

we solve this using quadratic formula giben by (-b+/- * sqrt(b^2-4ac))/2a

-4 +/- ((sqrt(4^4 -4*1*(-221)))/2

x= (-4 + sqrt(900))/2

x=( -4+ 30)/2

x=13

width =13

length =x+4 = 17

So the dimension of the den is 13 and 17

13*17=221

hence 13 and 17 are the dimensions

Answer 2

Create a system of equations for length (L) and width (W)

L = 4 + W

LW = 221

Substitute L in the first equation with L in second equation and find W

(4+W)W = 221

4W + W² = 221

W² + 4W - 221 = 0

(W+17)(W-13) = 0

W = -17, 13 (positive solution only!)

Use W to find L

L = 4 + W = 4 + 13 = 17

Hence, the dimensions of Janas' den are 17ft by 13ft! Hope this helped!