A triangle has side lengths of 3in, 4in, and 6in. The longest side of a similar triangle is 15 in. What is the length of the shortest side of the similar triangle?
The ratio of the sides of the 1st triangle is,
3 : 4 : 6
The second triangle is
x : x : 15
6 : 15 = 3 : x
6/15 = 3/x
cross multiply
6x = 45
x = 7.5
To find the length of the shortest side of the similar triangle, we can use the concept of similarity.
In similar triangles, the corresponding sides are proportional. This means that we can set up a proportion with the sides of the two triangles.
Let's call the length of the shortest side in the similar triangle "x inches".
Using the given information, we can set up the following proportion:
(3 inches) / x inches = (6 inches) / (15 inches)
To solve for x, we can cross-multiply:
3 inches * 15 inches = 6 inches * x inches
45 inches = 6x inches
Now, we can divide both sides of the equation by 6 inches to isolate x:
45 inches / 6 inches = x inches
7.5 inches = x
Therefore, the length of the shortest side of the similar triangle is 7.5 inches.
To find the length of the shortest side of the similar triangle, we can use the concept of similar triangles and their corresponding side lengths.
In similar triangles, corresponding sides are proportional. This means that if we have two similar triangles, the ratio of the lengths of corresponding sides will be the same.
Let's find the ratio of the corresponding sides of the two triangles. The longest side of the original triangle is 6 in, and the longest side of the similar triangle is 15 in. Therefore, the ratio of the longest sides is 15/6.
Now, we can set up a proportion to find the length of the shortest side of the similar triangle. We know that the shortest side of the original triangle is 3 in, and we want to find the length of the shortest side in the similar triangle.
3 in / x = 6 in / (15/6)
To simplify the proportion, we can multiply both sides by (15/6):
(15/6) * (3 in / x) = 6 in
Now, we can solve for x by cross-multiplying:
(15/6) * (3 in) = 6 in * x
Simplifying the left side:
(45/6) in = 6 in * x
Now, we can solve for x by dividing both sides by 6 in:
(45/6) in / 6 in = x
Simplifying:
7.5 in = x
Therefore, the length of the shortest side of the similar triangle is 7.5 in.