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The area of a trapezoid is 180 cm². The height is 18 cm and the length of one of the parallel sides is 5 cm. Find the length ofthe second parallel side. Express your answer as a simplified fraction or a decimal rounded to two places.

User White Owl
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The area of a trapezoid is given by:


A=(1)/(2)\cdot h\cdot(a+b).

Where:

• h is the heigh,

,

• a and b are the length of the parallel sides.

In this problem, we have:

• A = 180 cm²,

,

• h = 18 cm,

• a = 5 cm,

,

• b = x.

Replacing these data in the equation above, we have:


180cm^2=(1)/(2)\cdot18\operatorname{cm}\cdot(5\operatorname{cm}+x)\text{.}

Solving for x the last equation, we get:


\begin{gathered} \frac{2\cdot180cm^2}{18\operatorname{cm}}=5\operatorname{cm}+x, \\ 20\operatorname{cm}=5\operatorname{cm}+x, \\ x=20\operatorname{cm}-5\operatorname{cm}, \\ x=15\operatorname{cm}\text{.} \end{gathered}

So the length of the second parallel side is:


x=15\operatorname{cm}\text{.}

Answer: 15 cm

User Benzonico
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