Algebra 2 word problem involving quadratic formula.

Question

You have an 18 ft by 10ft garden. you are planning on doubling the gardens area by adding the same distance x to both the length and the width. What will be the new dimensions of the garden?

Answer 1

Hi Caroline,

 

Area = 18*10 = 180 ft²

 

You want

(18 +x)(10+x)= 2*Area

180 + 28x + x² =360

x² + 28x -180=0

 

use the quadratic formula

 

x = (-b ±√(b² -4ac))/2

 

a=1, b =28, c=-180

 

x=(-28± √(784+720))/2

  =(-28±√1504)/2   only the positive value represent a real length

 

x=(-28 + √1504)/2 = -14+√376

x=5.39 ft

Answer 2

(18 + x)(10 + x) = 2*18*10 = 360

 

x² + 28x + 180 = 360

 

x² + 28x - 180 = 0

 

Using the quadratic formula with a = 1, b = 28, c = -180

 

x = [-28 +/- sqrt(28² - 4*1*-180)]/2*1 = [-28 +/- 38.78]/2

 

Therefore x = 10.78/2 =   5.39 since using the negative sign for the second term makes no sense.

 

Check:  (18 + 5.39)(10 + 5.39) = 359.97

 

within rounding error.

 

So the new dimensions are 23.39 and 15.39

 

Earlier I used 8 rather than 18, sorry for the confusion.