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

Given:
- Height (H) = 8 cm
- Length (L) = 6 cm

A re a = 2 a re a o f ba se + 4 \area o f s i d e a re a o f ba se = 2 w i d t h ∗ L = 12 w i d t h a re a o f s i d e = 2 w i d t h ∗ 8 + 2 ∗ 6 ∗ 8 = 96 + 16 w i d t h 208 = 96 + 16 w i d t h + 12 w i d t h 208 = 96 + 28 w i d t h ∣ S u b t r a c t 96 112 = 28 w i d t h ∣ D i v i d e b y 28 w i d t h = 4 c m

Answered by luana | 2024-06-10

By definition, the surface area of a rectangular prism is given by: A = 2 wl + 2 w h + 2 h l Where, w: width of the prism h: prism height l: length of the prism Clearing w we have: A = 2 ( wl + w h + h l ) A = 2 w ( l + h ) + 2 h l w = 2 ( l + h ) A − 2 h l ​ Substituting values we have: w = 2 ( 6 + 8 ) 208 − 2 ( 8 ) ( 6 ) ​ Rewriting: w = 2 ( 14 ) 208 − 96 ​ w = 28 112 ​ w = 4 **Answer: ****the width of the rectangular prism is: ** w = 4

Answered by carlosego | 2024-06-11

The width of the rectangular prism is 4 cm. This is found using the surface area formula and substituting the given values for height and length. After rearranging and solving the equation, we determined the width to be 4 cm.
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Answered by carlosego | 2024-12-26