Question

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

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

$204.25=2(10\times x+x\times 6.5+6.5\times 10)$

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

$204.25=2(16.5x+65)$

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.

$\dfrac{74.25}{33}=x$

$2.25=x$

Therefore, the correct option is B.