The sides of a triangle are 4, 10, and 5. Find the length of the longest side of a similar triangle whose shortest side is 12.
In triangle 4 , 10 , 5 shortest side is 4 , longest side is 10
The ratio of corresponding shortest sides 12 / 4 = 3
The ratio of corresponding longest sides is also 3
3 ∙ 12 = 36
My typo.
3 ∙ 10 = 30
30 is longest side.
To find the length of the longest side of a similar triangle, we can use the concept of proportional sides.
In a similar triangle, the ratio of the lengths of corresponding sides is the same for all sides.
Let's find the ratio of the corresponding sides of the given triangle:
Shortest side in given triangle = 4
Shortest side in similar triangle = 12
Ratio of the shortest sides = 12/4 = 3
Using this ratio, we can find the length of the longest side of the similar triangle:
Longest side in given triangle = 10
Longest side in similar triangle = (Ratio) * (Longest side in given triangle)
Longest side in similar triangle = 3 * 10 = 30
Therefore, the length of the longest side of the similar triangle, whose shortest side is 12, is 30.
To find the length of the longest side of a similar triangle, we can use the concept of similarity ratios. Similar triangles have corresponding sides that are proportional to each other.
Let's call the length of the longest side of the similar triangle "x".
To establish a similarity ratio, we need to compare the corresponding sides of the original triangle and the similar triangle. In this case, we will use the shortest sides of each triangle.
The given shortest side of the original triangle is 4, and the shortest side of the similar triangle is 12. We can set up the following ratio:
4 / 12 = 5 / x
Next, we can simplify the ratio by cross-multiplying and solving for "x":
4x = 12 * 5
4x = 60
Dividing both sides of the equation by 4, we get:
x = 60 / 4
x = 15
Therefore, the length of the longest side of the similar triangle, given that its shortest side is 12, is 15.