Question

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

Answer 1

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