Answer:
Question #3: b = 12 in
Question #4: b = 14.1 in
Step-by-step explanation:
Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:
Height = 4 b
Width = 3 b
Depth = b
So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]
we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:
[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]
Question # 4:
The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:
Area of each lateral plank :
[tex](4b)\,(b) = 4\,b^2[/tex]
Then twice these is: [tex]8\, b^2[/tex]
So we can solve for be requesting that these total surface equal the amount of silk:
[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]
which rounded to the nearest tenth of an inch gives:
[tex]b\approx 14.1\,\,in[/tex]
