Question

Two similar triangles have corresponding sides measuring 8 inches and 12 inches. If the altitude of the smaller triangle is 6 inches, what is the length of the corresponding altitude of the larger triangle?

a) 9 inches
b) 18 inches
c) 24 inches
d) 16 inches

Answer 1

To find the length of the corresponding altitude of the larger triangle, we can set up a proportion using the given information. By cross multiplying and solving for x, we find that the length of the corresponding altitude of the larger triangle is 9 inches.

Step-by-step explanation:

In this problem, we are given two similar triangles with corresponding sides measuring 8 inches and 12 inches. We are also given the altitude of the smaller triangle, which is 6 inches. Since the triangles are similar, the ratio of their corresponding sides is equal to the ratio of their corresponding altitudes. Therefore, we can set up a proportion to find the length of the corresponding altitude of the larger triangle:

6 inches / 8 inches = x inches / 12 inches

To solve for x, we can cross multiply:

6 inches * 12 inches = 8 inches * x inches

72 inches = 8 inches * x inches

To isolate x, we can divide both sides of the equation by 8 inches:

x inches = 72 inches / 8 inches

x inches = 9 inches