Question

Find the width of the rectangular prism when the surface area is 208 centimeters

Answer 1

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

(

d

w

+

h

w

+

h

d

)

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

(

d

w

+

h

w

+

h

d

)

208

=

2

[

6

w

+

8

w

+

(

8

)

(

6

)

]

208

=

2

(

14

w

+

48

)

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

208

=

2

(

14

w

+

48

)

208

=

28

w

+

96

112

=

28

w

112

28

=

w

4

=

w

The width is

4

.

Answer 2

Given that length is 6 cm, height is 8cm and surface area is 208 square meter, the width of the rectangular prism is 4 centimeters.

How to find the width of the rectangular prism

To find the width of the rectangular prism when the surface area is 208 square centimeters, use the formula for the surface area of a rectangular prism.

The formula for the surface area of a rectangular prism is:

Surface Area = 2lw + 2lh + 2wh

Given:

Length (l) = 6 cm

Height (h) = 8 cm

Surface Area = 208 square centimeters

Substitute the given values into the formula

208 = 2(6)(w) + 2(6)(8) + 2(w)(8)

Simplifying the equation:

208 = 12w + 96 + 16w

Combining like terms:

208 = 28w + 96

Rearranging the equation:

28w = 208 - 96

28w = 112

Dividing both sides by 28:

w = 112 / 28

w = 4

Therefore, the width of the rectangular prism is 4 centimeters.