A triangle has sides of lengths 4.2, 5.7, and 7.2 inches. The smallest side of a similar triangle is 1.4 inches. What are the lengths of the other two sides? Write the smaller side length first and the larger side length second.
the smaller side length is what inches? and the larger side length is what inches?
The ratio of the sides of the larger triangle to the sides of the smaller triangle is equal to the ratio of the corresponding sides of similar triangles.
Let's represent the sides of the smaller triangle as 1.4x, where x is the ratio of the side lengths. So, the sides of the larger triangle are 4.2x, 5.7x, and 7.2x.
Given that the smallest side of the larger triangle is 1.4 inches, we can set up the following equation:
1.4 = 1.4x
Dividing both sides by 1.4:
x = 1
Therefore, the ratio of the sides of the similar triangles is 1:1.
Thus, the lengths of the sides of the larger triangle are:
Smaller side length: 4.2 inches
Larger side length: 7.2 inches
that was wrong bot
I apologize for the incorrect response. Let's reassess the problem.
The given triangle has sides of lengths 4.2, 5.7, and 7.2 inches. We need to find the corresponding sides of a similar triangle with a smallest side length of 1.4 inches.
To find the ratio between the corresponding sides of the two triangles, we can divide the smallest side length of the larger triangle by the smallest side length of the smaller triangle:
1.4 / 4.2 = 1/3
Therefore, the ratio of the sides of the similar triangles is 1/3.
Now, we can calculate the lengths of the other two sides of the larger triangle:
Smallest side length: 1.4 inches
Middle side length: 1.4 × 5.7 = 7.98 inches
Largest side length: 1.4 × 7.2 = 10.08 inches
So, the smaller side length is 1.4 inches, and the larger side length is 10.08 inches.
wrong again bot
Apologies for the incorrect response. Let's try solving it again.
The given triangle has sides of lengths 4.2, 5.7, and 7.2 inches. We need to find the corresponding sides of a similar triangle with a smallest side length of 1.4 inches.
To find the ratio between the corresponding sides of the two triangles, we divide the smallest side length of the larger triangle by the smallest side length of the smaller triangle:
x = 1.4 / 4.2 = 1/3
Therefore, the ratio of the sides of the similar triangles is 1/3.
Now, we can find the lengths of the other two sides of the larger triangle:
Smallest side length: 1.4 inches
Middle side length: 1.4 * 5.7 = 7.98 inches
Largest side length: 1.4 * 7.2 = 10.08 inches
So, the smaller side length is 1.4 inches, and the larger side length is 10.08 inches.