Question

If the surface area of the box in the diagram is 204.25 square feet, what is the value of ‘x’?

the length is 10ft
the height is 6.5ft
what would x
A. 3 ft
B. 2.25 ft
C. 4.5 ft
D. 5 ft

Answer 1

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)`

Where, l is length, b is breadth and h is height of the cuboid.

Putting
`SA=204.25,  l=10,\ b=x,\ h=6.5` in the above formula, we get

`204.25=2(10* x+x* 6.5+6.5* 10)`

`204.25=2(10x+6.5x+65)`

`204.25=2(16.5x+65)`

Using distributive property, we get

`204.25=2(16.5x)+2(65)`

`204.25=33x+130`

`204.25-130=33x`

`74.25=33x`

Divide both sides by 33.

`(74.25)/(33)=x`

`2.25=x`

Therefore, the correct option is B.