The ratio of the lengths of the sides of a triangle is 3:8:9.
The longest side of a second, similar triangle is 15 cm in
length. What is the length, in centimeters, of the shortest
side of the second triangle?
F.
5
G.
6
H.
9
J.
10
K.
The length cannot be determined based on the
information given.
To find the length of the shortest side of the second triangle, we need to first determine the ratio of the sides of the second triangle.
Since the ratio of the sides of the first triangle is 3:8:9, we can multiply each term by a constant to find the actual lengths. Let the lengths of the sides of the first triangle be 3x, 8x, and 9x.
For the second triangle, we are told that the longest side is 15 cm. Since we are dealing with similar triangles, the ratio of the sides of the second triangle must also be in the same ratio of 3:8:9. Let the lengths of the sides of the second triangle be 3y, 8y, and 9y.
Given that the longest side of the second triangle is 15 cm, we can set up an equation:
9y = 15
y = 15/9
y = 5/3
To find the length of the shortest side of the second triangle, we can simply multiply the ratio term by y:
Shortest side = 3y = 3 * (5/3) = 5 cm
Therefore, the length of the shortest side of the second triangle is 5 cm. The answer is F. 5.