A pole of actual height, H, 3.1m casts a shadow of 1.25m
Let the height of the building be x which casted a shadow of height 50,25m
The ratio of the actual height to the shadow height of the pole is
[tex]\text{Ratio}=\frac{\text{Actual height of pole}}{Shadow\text{ height of pole}}=\frac{3.1}{1.25}[/tex]
The ratio of the actual height to the shadow height of the building is
[tex]\text{Ratio}=\frac{\text{Actual height of building}}{Shadow\text{ height of building}}=\frac{x}{50.25}[/tex]
The proportion of both ratio is
[tex]\frac{3.1}{1.25}=\frac{x}{50.25}[/tex]
Crossmultiply to find the value of x
[tex]\begin{gathered} \frac{3.1}{1.25}=\frac{x}{50.25} \\ 1.25x=3.1\times50.25 \\ \text{Divide both sides by 1.25} \\ \frac{1.25x}{1.25}=\frac{155.775}{1.25} \\ x=124.62m \\ x=125m\text{ (nearest meter}) \end{gathered}[/tex]
Hence, the height of the building is 125m (nearest meter)
