Question

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 5x\\ w& 4x\\ h& 3x\\ \text{L.A.}& \\ \text{T.A.}& \\ V& \end{array}$

Short answer

\begin{align} l & = 5x\\w &= 4x\\ h&=3x\\L.A.&=54 x^2\\T.A. &= 94x^2\\V&=60x^3\end{align}

Step-by-step solution

Step 1. Given information.

The length, width and height of a rectangle are 5x, 4x and 3x respectively.

Step 2. Write the concept.

The lateral area of the rectangle is given by:

$\text{L.A.}=\text{Perimeter}\times \text{Height}$

The total area of the rectangle is given by:

$\text{T.A.}=\text{L.A.+}2\left(\text{Base}\right)$

The volume of rectangle is given by:

$\text{V}=l\times w\times h$

Step 3. Determine the value.

Now, substitute all the given values in the formula.

$\begin{array}{c}\text{L.A.}=2(l+w)\times h\\ =2(5x+4x)\times 3x\\ =2\left(9x\right)\times 3x\\ =18x\times 3x\\ =54x^2{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And

$\begin{array}{c}\text{T.A.}=54x^2\text{+}2(5x\times 4x)\\ =54x^2\text{+}2\left(20x^2\right)\\ =54x^2{\text{+40x}}^2\\ =94x^2{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And the volume is

$\begin{array}{c}\text{V}=5x\times 4x\times 3x\\ =20x^2\times 3x\\ =60x^3{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$