For each of the following, the Surface Area is given. Calculate the missing dimension.

This is a rectangular prism with the width missing. The height seems to be 20 cm. The length I guess is 34 cm, and the Surface Area is 6020cm square. How do I find the missing width? I checked in the back of the book for the answer and it said 43.1. I have no clue how they came up with that.

Also the formula my teacher gave me to find the surface area of this dimension is....

SA = 2lw + 2lh+ 2wh.

I just don't get how to find the missing dimension. Please Help.

Just plug in your given values into the equation

6020 = 2(34)w + 2(34)(20) + 2(w)(20)
6020 = 68w + 1360 + 40w
4660 = 108w
w = 43.148 , your answer

Thanks a lot Reiny! I love your help.

your are welcome

May I suggest you use a "nickname" instead of "anonymous"
If you use the same computer each time you will not have to type it each time.

To find the missing width, you can use the formula for the surface area of a rectangular prism, which your teacher provided: SA = 2lw + 2lh + 2wh.

In this case, you have the surface area (SA) of 6020 cm², the length (l) of 34 cm, and the height (h) of 20 cm. You need to find the missing width (w).

Let's rearrange the formula to isolate the width (w):

SA = 2lw + 2lh + 2wh
6020 = 2(34)w + 2(34)(20) + 2w(20)
6020 = 68w + 1360 + 40w
6020 = 108w + 1360
6020 - 1360 = 108w
4660 = 108w

To find the value of w, divide both sides of the equation by 108:
w = 4660 ÷ 108 = 43.15 (rounded to two decimal places)

So, the missing width is approximately 43.15 cm.

Note that the answer you found in the back of the book, 43.1 cm, is likely an approximation or rounded value.

Remember to double-check your calculations and make sure you've accurately entered the values into the equation.