Question

the area of a window is 192 in squared. The width if the window is four inches more than half the length of the window. What are the dimensions of the window?

Answer 1

Answer:

Length = 16 inches and width = 12inches

Step-by-step explanation:

A = 192 in² . The width is 4 + 1/2x.  therefore let x = length

Area = LW

192 =  x(4 + 1/2 x)

192 = 4x + 1/2x²      

384 = 8x  + x²                            Multiply each term by 2 to make a  

384 + 16 =  x² + 8x + 16              Complete the square

400 = (x  + 4)²        

$\sqrt{400} = \sqrt{(x + 4)^2}$

± 20 = x + 4

20 = x + 4  or  -20 = x + 4

20 - 4 = x     or  -20 - 4 = x

    16 = x   or   -24 = x   reject the negative amount

   Length = 16

   width = 4 + 1/2(16);   4 + 8 = 12