Question

8) The height of a building h varies directly as the length and inversely as the width, if h = 25m when l = 10m and w = 5m, find the width when h = 50m and I remains the same

Answer 1

Let h,l, and w represent the height, length, and width of the building respectively

Then

$\begin{gathered} h\text{ = }\frac{kl}{w} \\ \text{where k is the constant of proportionality} \end{gathered}$$\begin{gathered} \Rightarrow k=\frac{hw}{l} \\ \Rightarrow k=\frac{25\times5}{10}=12.5 \end{gathered}$$\Rightarrow h=\frac{12.5l}{w}$

The new value of h = 50m, but l remains the same.

That is l = 10m

Therefore

$\begin{gathered} \frac{50}{1}=\frac{12.5\times10}{w} \\ \Rightarrow\frac{50}{1}=\frac{125}{w} \\ \text{Cross multiplying, we have} \\ 50w\text{ = 125} \\ \Rightarrow\text{ w=}\frac{125}{50}=2.5 \end{gathered}$

Hence, the width is 2.5m