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**Hint:**For answering this question we will use the given information in the question which is given us the height of a room is “$a$” and the areas of the two adjacent walls of a room are “$b$” and “$c$”. And use the concept from the basics which is stated as for a room we will have length $l$ , breadth $b$ and height $h$. The area of one wall be $lh$ and the other wall be $bh$ and the area of the roof will be $lb$.

**Complete step-by-step solution:**

Now considering from the question we have been given that, the height of the room will be $a$ . And the areas of the two adjacent walls are respectively “$b$” and “$c$”.

Let us assume that the length of the wall be $x$ and the breadth of the wall be $y$

From the question given that the areas of the two adjacent walls are respectively “$b$” and “$c$” respectively.

From the basics we know the concept which is stated as for a room we will have length $l$ , breadth $b$ and height $h$. The area of one wall be $lh$ and the other wall be $bh$ and the area of the roof will be $lb$.

Therefore the area of one wall will be given as $x\times a=b$.

So we can say that $x=\dfrac{b}{a}$ .

And similarly,

$\begin{align}

& y\times a=c \\

& \Rightarrow y=\dfrac{c}{a} \\

\end{align}$

Hence, we can say that the area of the roof will be the product of the length of the wall and breadth of the wall.

Given as,

$\begin{align}

& \text{Area of the roof}=x\times y \\

& \Rightarrow \dfrac{b}{a}\times \dfrac{c}{a} \\

& \Rightarrow \dfrac{bc}{{{a}^{2}}} \\

\end{align}$

Therefore we can conclude that when the height of a room is “$a$” and the areas of the two adjacent walls of a room are “$b$” and “$c$” then the area of the roof will be $\dfrac{bc}{{{a}^{2}}}$ .

**Hence, option D is the correct option.**

**Note:**While answering questions of this type we should be sure with calculations and the concept. From the basic concept we know that for a room we will have length $l$ , breadth $b$ and height $h$ . The area of one wall be $lh$ and the other wall be $bh$ and the area of the roof will be $lb$ .

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