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{ = }(kl)/(w) \\ \text{where k is the constant of proportionality} \end{gathered}`
`\begin{gathered} \Rightarrow k=(hw)/(l) \\ \Rightarrow k=(25*5)/(10)=12.5 \end{gathered}`
`\Rightarrow h=(12.5l)/(w)`

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

That is l = 10m

Therefore

`\begin{gathered} (50)/(1)=(12.5*10)/(w) \\ \Rightarrow(50)/(1)=(125)/(w) \\ \text{Cross multiplying, we have} \\ 50w\text{ = 125} \\ \Rightarrow\text{ w=}(125)/(50)=2.5 \end{gathered}`

Hence, the width is 2.5m