The length of an open-top box is 4 cm longer than its width. The box was made from a 480-cm^2 rectangle sheet of material with 6 cm-by-6 cm squares cut from each corner. The height of the box is 6 cm. Find the dimensions of the box.
+128474 Since four 6 x 6 squares were cut from the original, sheet, the new surface area is given by:
480 - 4(6 x 6) = 480 - 36(4) = 480 - 144 = 336 cm^2
And the surface area of the box is given by
2[W + (W + 4)]6 = 336 where W is the width and W + 4 is the length...so we have
2[ 2W + 4]6 = 336
12[2W + 4] = 336 divide both sides by 12
2W + 4 = 28 subtract 4 from both sides
2W = 24 divide both sides by 2
W = 12cm this is the width
W + 4 = 12 + 4 = 16cm this is the length
+128474 Since four 6 x 6 squares were cut from the original, sheet, the new surface area is given by:
480 - 4(6 x 6) = 480 - 36(4) = 480 - 144 = 336 cm^2
And the surface area of the box is given by
2[W + (W + 4)]6 = 336 where W is the width and W + 4 is the length...so we have
2[ 2W + 4]6 = 336
12[2W + 4] = 336 divide both sides by 12
2W + 4 = 28 subtract 4 from both sides
2W = 24 divide both sides by 2
W = 12cm this is the width
W + 4 = 12 + 4 = 16cm this is the length
