Question

The total surface area of a rectangular prism is $900{\text{ft}}^2$. The length and breadth of this prism is $15ft$ and $10ft$ resepctively. Find the depth of this rectangular prism.

• A. 12 ft
• B. 15 ft
• C. 24 ft
• D. 6 ft

Answer 1

The correct option is A 12 ft

Let's draw a rectangular prism with appropriate dimensions.
Given,
Length of the rectangular prism $l=15$ ft

Breadth of the rectangular prism $b=10$ ft

Depth of the rectangular prism $h=x$ ft

Total surface area of the rectangular prism $=900{\text{ft}}^2$

As we know,
The total surface area of a rectangular prism $=2\left(lb\right)+2\left(bh\right)+2\left(lh\right)$

$900=(2\times 15\times 10)+(2\times 10\times x)+(2\times 15\times x)$

$900=300+20x+30x$

$900-300=50x$

$600=50x$

$x=\frac{600}{50}=12ft$

Hence, depth of the rectangular prism $x=12$ ft
option (a) is correct.