Trapezoid

The area of a trapezoid is 135 cm². The sides a, c, and height h are in a ratio of 6:4:3. How long are sides a, c, and height h? Perform calculation.

Correct answer:

a =  18 cm
c =  12 cm
h =  9 cm

Step-by-step explanation:

$$\begin{gathered} S=135{\text{cm}}^2 \\ a:c:h=6:4:3=6x:4x:3x \\ S=\frac{a+c}{2}\cdot h \\ S=\frac{6x+4x}{2}\cdot 3x \\ S=15x^2 \\ x=\sqrt{S/15}=\sqrt{135/15}=3\text{cm} \\ a=6\cdot x=6\cdot 3=18\text{cm} \end{gathered}$$

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

$h=3\cdot x=3\cdot 3=9\text{cm}$

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