What is the width of a rectangular prism when the surface area is 208 square centimeters, and it has a height of 8 and a depth of 6?

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Answer 1 · 2018-05-21T12:14:11

The width is #4#.

Use the surface area formula of a rectangular prism to find the width. (I have changed it to use the same terms given in the problem).

#A = 2(dw + hw + hd)#

Because of the given information, it is known that:

#A = 208#
#h = 8#
#d = 6#

The width is not know, so let it keep it's variable #w#. But substitute the other values into the equation:

#A = 2(dw + hw + hd)#

#208 = 2[6w + 8w + (8)(6)]#

#208 = 2(14w + 48)#

Use the distributive property to solve the right side of the equal sign:

#208 = 2(14w + 48)#

#208 = 28w + 96#

#112 = 28w#

#112/28 = w#

#4 = w#

The width is #4#.