Question

The areas of two similar triangles are 121 cm² and 100 cm². If the altitude of a larger triangle is 6.6 cm, then the corresponding altitude of the smaller triangle is ______.

Options

• 5.5 cm

• 5 cm

• 6 cm

• 4.4 cm

Answer 1

The areas of two similar triangles are 121 cm² and 100 cm². If the altitude of a larger triangle is 6.6 cm, then the corresponding altitude of the smaller triangle is 6 cm.

Explanation:

For similar triangles, the ratio of areas is equal to the square of the ratio of corresponding sides (or altitudes):

`"Area"_1/"Area"_2 = (h_1/h_2)^2`

Let the larger triangle area = 121, the smaller = 100, and the altitude of the larger = 6.6 cm.

`121/100 = (6.6/h)^2`

`6.6/h = sqrt(121/100)`

`6.6/h = 11/10`

`h = 6.6 xx 10/11`

∴ h = 6 cm