Answer:
31.6in
Step-by-step explanation:
A department store stocks gift boxes for the holiday season. The box has a volume of 500 cubic inches. You also know that the length of the box is 9 inches longer than the width and the height 1/2 as long as the width
Volume of the box = Length * Width * Height
Given
Volume = 500in³
If the length of the box is 9 inches longer than the width, then;
L = W+9
Also if the height is 1/2 as long as the width, then;
H = 1/2 W
Substtute into the volume formula;
V = LWH
500 = (W+9)W(1/2W)
500 = W+9(W²/2)
1000 = W²(W+9)
1000 =W³+9W²
W³+9W² - 1000 = 0
Factorize AND GET w
W³+9W² = 1000
w²(W+9) = 1000
W² = 1000
w = √1000
w = 31.6in
Hence the width of the store is 31.6in
Note that we only looked for the width since are not told what to find
