Question

The area of two similar triangles are 18cm^2 and 8cm^2. ONe of the sides of the first triangle is 4.5cm. What is the length of the corresponding side of the other triangle.

Answer 1

If two triangles are similar, the ratio of their corresponding side lengths is the same as the ratio of their areas.

We know that the area of the first triangle is 18 cm^2, and the area of the second triangle is 8 cm^2. So, the ratio of their areas is 18/8 = 9/4

We also know that one of the sides of the first triangle is 4.5 cm.

So the ratio of the corresponding side of the second triangle to the first triangle is:

(length of corresponding side of second triangle) / 4.5 = 9/4

We can cross-multiply and solve for the length of the corresponding side of the second triangle:

4.5 * (9/4) = 9 * (9/4) / 4 = 9 * 2.25 / 4 = 20.25 / 4 = 5.0625 cm

So, the length of the corresponding side of the second triangle is 5.0625 cm.