The lengths of the sides of a triangle are 6,7, and 9. What is the longest side of a similar triangle whose shortest side is 4.
6:7:9 = 4:?:x
x/9 = 4/6
x =(4/6)(9) = 6
20
To find the longest side of a similar triangle, we need to determine the scale factor between the two triangles. The scale factor is the ratio of corresponding side lengths.
Given that the shortest side of the original triangle is 6 and the corresponding shortest side of the similar triangle is 4, we can calculate the scale factor as follows:
Scale factor = (shortest side length of similar triangle) / (shortest side length of original triangle)
Scale factor = 4 / 6
Scale factor = 2/3
Now, we can use the scale factor to find the longest side of the similar triangle:
Longest side of similar triangle = (scale factor) * (longest side of original triangle)
Longest side of similar triangle = (2/3) * 9
Longest side of similar triangle = 6
Therefore, the longest side of the similar triangle is 6.
To find the longest side of a similar triangle, we can use the concept of proportions. Similar triangles have corresponding sides that are proportional to each other.
First, let's find the ratio of the corresponding sides. We'll take the longest side of the original triangle and divide it by the shortest side:
Ratio = (longest side of original triangle) / (shortest side of original triangle)
= 9 / 6
= 3 / 2
Now, let's use this ratio to find the longest side of the similar triangle. We'll multiply the shortest side of the similar triangle by the ratio we found:
Longest side of similar triangle = (shortest side of similar triangle) * Ratio
= 4 * (3 / 2)
= 12 / 2
= 6
Therefore, the longest side of the similar triangle, when the shortest side is 4, is 6.