Question

The surface area of a rectangular prism is found using the formula SA = 2(lw + lh + wh), where l is length, w is width, and h is height. If the surface area of a rectangular prism is 324km^2
, with length 5 m and width 12 m, what is the height, in meters?

Answer 1

⇒ Solutions 

To solve the given problem you first have to plug all the numbers in....

324 m² is the SA so 324 m² = 2[(5m × 12m) + (5m × h) + (12m × h)]
 
You want to find the variable h so first start by dividing 342 by 2 which will make your equation simpler to solve.

= 162 m² = (5m × 12m) + (5m × h) + (12m × h)

Multiply your "lw" together 5m × 12m = 60m² and you have

162 m² = 60 m² + (5m × h) + (12m × h)
 
You can subtract 162 m² by 60 m² leaving 102 m² = (5m × h) + (12m × h)

Then combine your like terms of h....5m × h + 12m × h = 17m × h so you now have 102m² = 17m × h and to get (h) by itself to solve for it you can then divide by 17 leaving 6m = (h) making your height equal 6 meters.

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(SA/2 - lw) = (h(l+w) ...... Subtract terms not containing (h)
 
(SA/2 - lw) ÷ (l+w) = (h) ..... Divide by the coefficient of (h) 

(324/2 - 5 × 12) ÷ (5+12) = (h) ...  Plug in the numbers 

(162 - 60) ÷ 17 = (h) = 6 ... Answer