Question

The ratio of the areas of two similar
parallelograms is 4:9. Find the height of the
bigger one if the smaller is of height 4cm.
​

Answer 1

Answer: 6 cm

Step-by-step explanation:

Given: The ratio of the areas of two similar  parallelograms is 4:9.

To find : The height of the  bigger one if the smaller is of height 4 cm.

Let h be the height of the  bigger one.

Since the areas of similar figures are proportional to the square of their corresponding sides.

Then, $\dfrac{4^2}{h^2}=\dfrac{4}{9}$

$\dfrac{16}{h^2}=\dfrac{4}{9}\\\\\Rightarrow\ h^2=\dfrac{9}{4}\times16\\\\\Rightarrow\ h^2=36\\\\\Rightarow\ h= 6\ cm\ \ \ \ \text{[ height cannot be negative.]}$

Hence, the height of bigger parallelogram = 6 cm