Question

The areas of two similar triangles are 144 unit2 and 81 unit2. What is the ratio of their perimeters? If a side of the first is 6 units long, what is the length of the corresponding side of the second?

A) 3:4, 4.5 units
B) 4:3, 2 units
C) 3:4, 3 units
D) 4:3, 9 units

Answer 1

The ratio of the perimeters is 4:3. The corresponding side of the second triangle is 8 units.

Step-by-step explanation:

To find the ratio of the perimeters of two similar triangles, we first need to find the ratio of their side lengths, since the perimeters depend on the lengths of the sides. We can do this by taking the square roots of the ratios of their areas. So, in this case, the ratio of the perimeters is the square root of the ratio of the areas: √(144/81) = √(16/9) = 4/3.

If a side of the first triangle is 6 units long, we can use the ratio we found to find the length of the corresponding side of the second triangle. The ratio of their side lengths is 4/3, so the length of the corresponding side of the second triangle is (4/3) * 6 = 24/3 = 8 units.