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san4es73 [151]
2 years ago
11

The heights of two similar parallelograms are 16 inches and 20 inches. Their

Mathematics
1 answer:
Fittoniya [83]2 years ago
3 0

Answer: x=\dfrac{25}{21}

Step-by-step explanation:

Area of parallelogram = Base x height

If two parallelograms are similar, then their corresponding sides are proportional.

That means, \dfrac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\dfrac{\text{height of first parallelogram}}{\text{height of second parallelogram}}

\Rightarrow \dfrac{3x+5}{9x}=\dfrac{16}{20}\Rightarrow \dfrac{3x+5}{9x}=\dfrac{4}{5}\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=\dfrac{25}{21}

Hence, x=\dfrac{25}{21}

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