The outside of a picture frame measures 8 in by 17 in. 52 insquared2 of the picture shows. Find the thickness of the frame.

Question

The thickness of the frame is
how many inches

Answer 1

Usually, draw a picture:

 

     xxxxxxxxxx

     xyyyyyyyyx

     xyyyyyyyyx

     xyyyyyyyyx

     xyyyyyyyyx

     xxxxxxxxxx

The area showing is 52 sq. in.

 

The area showing is:   l*w = (8-x-x)*(17-x-x) = 52

     (8-2x)((17-2x) = 52

     136 - 16x - 34x + 4x² = 52             [F-O-I-L]

     4x² - 50x + 84 = 0                           [collect terms and re-arrange to have 0 on right side]

 

    (2x-4)(2x-21) = 0                     [either factor or use quadratic formula]

 

Either 2x-4=0  or  2x-21=0    or both          [Multiplicative Property of Zero]

 

Either x = 2, so the area showing is:  4 in by 13 in   [52 sq in]

    or

         x=10.5, so the area showing is:     (-13) in by (-4) in   [also 52 sq in, but quite impossible]

      The frame is 2 inches wide.

Answer 2

The 52 in² picture area is in dimensions

(8-2x)(17-2x) where x is the thickness

of the frame:

 

(8-2x)(17-2x) = 52

136 - 16x - 34x + 4x² = 52

4x² - 50x + 84 = 0

2x² - 25x + 42 = 0

From quadraric equation

x = [25 ±√((-25)²-4(2)(42))]/(2(2))

x = (25 ±√289)/4

x = (25 ± 17)/4 

x = 21 or 2

 

The frame is 2 inches wide