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sladkih [1.3K]
4 years ago
11

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?
Mathematics
1 answer:
Arlecino [84]4 years ago
5 0
⇒ Solutions 

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

324 m</span>²<span> is the SA so 324 m</span>²<span> = 2[(5m </span>× <span>12m) + (5m </span>× <span>h) + (12m </span>× <span>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 m</span>²<span> = (5m </span>× <span>12m) + (5m </span>× <span>h) + (12m </span>× <span>h)

Multiply your "lw" together 5m </span>× <span>12m = 60m</span>²<span> and you have

162 m</span>² <span>= 60 m</span>²<span> + (5m </span>× <span>h) + (12m </span>× <span>h)
 
You can subtract 162 m</span>²<span> by 60 m</span>²<span> leaving 102 m</span>²<span> = (5m </span>× <span>h) + (12m </span>× <span>h)

Then combine your like terms of h....5m </span>× <span>h + 12m </span>× <span>h = 17m </span>× <span>h so you now have 102m</span>²<span> = 17m </span>× <span>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.
</span>
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(SA/2 - lw) = (h(l+w) ...... Subtract terms not containing (h)
 
(SA/2 - lw) ÷ <span>(l+w) = (h) ..... Divide by the coefficient of (h) </span>

(324/2 - 5 × 12) ÷ <span>(5+12) = (h) ...  Plug in the numbers 
</span>
(162 - 60) ÷ <span>17 = (h) = 6 ... Answer </span>
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