Note: Consider x be the breadth of the box.
Given:
The surface area of the box is 204.25 square feet.
Length of the box = 10 ft
Breadth of the box = x ft
Height of the box = 6.5 ft
To find:
The value of x.
Solution:
The surface area of a cuboid is:
![SA=2(lb+bh+hl)](https://tex.z-dn.net/?f=SA%3D2%28lb%2Bbh%2Bhl%29)
Where, l is length, b is breadth and h is height of the cuboid.
Putting
in the above formula, we get
![204.25=2(10\times x+x\times 6.5+6.5\times 10)](https://tex.z-dn.net/?f=204.25%3D2%2810%5Ctimes%20x%2Bx%5Ctimes%206.5%2B6.5%5Ctimes%2010%29)
![204.25=2(10x+6.5x+65)](https://tex.z-dn.net/?f=204.25%3D2%2810x%2B6.5x%2B65%29)
![204.25=2(16.5x+65)](https://tex.z-dn.net/?f=204.25%3D2%2816.5x%2B65%29)
Using distributive property, we get
![204.25=2(16.5x)+2(65)](https://tex.z-dn.net/?f=204.25%3D2%2816.5x%29%2B2%2865%29)
![204.25=33x+130](https://tex.z-dn.net/?f=204.25%3D33x%2B130)
![204.25-130=33x](https://tex.z-dn.net/?f=204.25-130%3D33x)
![74.25=33x](https://tex.z-dn.net/?f=74.25%3D33x)
Divide both sides by 33.
![\dfrac{74.25}{33}=x](https://tex.z-dn.net/?f=%5Cdfrac%7B74.25%7D%7B33%7D%3Dx)
![2.25=x](https://tex.z-dn.net/?f=2.25%3Dx)
Therefore, the correct option is B.