The corresponding altitude of two similar triangle are 8cm and 5cm. find the ratio of their areas
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.
Let the ratio of the side lengths of the triangles be x.
Since the corresponding altitudes of the triangles are 8cm and 5cm, the corresponding side lengths are in the same ratio as the altitudes: 8cm/5cm = x.
The ratio of the areas is therefore x^2.
To find x, we can set up the following proportion:
8cm/5cm = x
Cross multiplying, we get:
8cm * 5cm = 5cm * x
40cm^2 = 5cm * x
40cm^2 = 5x
x = 40cm^2 / 5
x = 8cm
Therefore, the ratio of the areas of the two similar triangles is 8^2 = 64.
The ratio of their areas is 64:1.