The ratio of the areas of two similar parallelogram is 4:9.find the height of the bigger one if the smaller one has 8cm height.
well, the ratio of sides is 2:3, so ...
To find the height of the larger parallelogram, we can use the ratio of the areas.
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides.
In this case, the ratio of the areas of the two parallelograms is given as 4:9.
Therefore, the ratio of their corresponding sides is the square root of 4:9, which is 2:3.
Since the height of the smaller parallelogram is given as 8 cm, we can calculate the height of the larger parallelogram by multiplying the height of the smaller one by the corresponding sides ratio.
Height of the larger parallelogram = Height of the smaller parallelogram * corresponding sides ratio
= 8 cm * (3/2)
= 12 cm
Therefore, the height of the larger parallelogram is 12 cm.
The answer
Since the areas of similar figures are proportional to the square of their corresponding sides
the sides are in the ratio of 2 : 3
x/8 = 3/2
2x = 24
etc