Trapezoid RT

The plot is a rectangular trapezium ABCD, where ABIICD has a right angle at the vertex B side and AB has a length of 36 m. The lengths of the sides AB and BC are in the ratio 12:7. The lengths of the sides AB and CD are in the ratio 3:2. Calculate the consumption mesh for the fence plot.

Correct answer:

x =  105.19 m

Step-by-step explanation:

$$\begin{gathered} AB=36\text{m} \\ AB:BC=12:7 \\ AB:CD=3:2 \\ 7AB=12BC \\ BC=\frac{7}{12}\cdot AB=\frac{7}{12}\cdot 36=\frac{7\cdot 36}{12}=\frac{252}{12}=21\text{m} \\ CD=\frac{2}{3}\cdot AB=\frac{2}{3}\cdot 36=\frac{2\cdot 36}{3}=\frac{72}{3}=24\text{m} \\ A{D}^2=B{C}^2+(AB-CD{)}^2 \\ AD=\sqrt{B{C}^2+(AB-CD{)}^2}=\sqrt{21^2+(36-24{)}^2}=3\sqrt{65}\text{m}\doteq 24.1868\text{m} \\ x=AB+BC+CD+AD=36+21+24+24.1868=105.19\text{m} \end{gathered}$$

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