Trapezium

The length of the base and the height size of the trapezium base are at a ratio of 5:3:2. The trapezium area is 128 cm². Calculate the length of the base and the height of the trapezoid.

Final Answer:

a =  20 cm
c =  12 cm
v =  8 cm

Step-by-step explanation:

$$\begin{gathered} a:c:v=5:3:2 \\ S=128{\text{cm}}^2 \\ S=\frac{a+c}{2}\cdot v \\ S=\frac{5k+3k}{2}\cdot 2k \\ S=4k\cdot 2k \\ S=8k^2 \\ k=\sqrt{S/8}=\sqrt{128/8}=4 \\ a=5k=5\cdot 4=20\text{cm} \end{gathered}$$

$c=3k=3\cdot 4=12\text{cm}$

$$\begin{gathered} v=2k=2\cdot 4=8=8\text{cm} \\ \text{ Verifying Solution: } \\ {S}_1=\frac{a+c}{2}\cdot v=\frac{20+12}{2}\cdot 8=128{\text{cm}}^2 \end{gathered}$$

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