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.(1 point)
The smaller side length is
inches and the larger side length is
inches.
To find the lengths of the other two sides of the similar triangle, we can use the concept of scaling.
Let's denote the lengths of the corresponding sides of the similar triangle as x and y. The ratio of corresponding side lengths in similar triangles is equal.
The ratio of the smaller side lengths is given as:
1.4 / 4.2 = x / 5.7
Cross-multiplying, we get:
1.4 * 5.7 = 4.2 * x
7.98 = 4.2x
x = 7.98 / 4.2
x ≈ 1.9
Similarly, the ratio of the smaller side lengths is given as:
1.4 / 4.2 = y / 7.2
Cross-multiplying, we get:
1.4 * 7.2 = 4.2 * y
10.08 = 4.2y
y = 10.08 / 4.2
y ≈ 2.4
Therefore, the lengths of the other two sides of the similar triangle are approximately 1.9 inches and 2.4 inches.
The smaller side length is 1.9 inches, and the larger side length is 2.4 inches.
To find the lengths of the other two sides of a similar triangle, you can use the concept of similarity ratios. The lengths of the sides of two similar triangles are proportional to each other.
Given that the smallest side of the original triangle is 4.2 inches and the smallest side of the similar triangle is 1.4 inches, we can set up a proportion:
(original triangle side length) / (similar triangle side length) = (original triangle side length) / (similar triangle side length)
Using the given values, the proportion becomes:
4.2 / 1.4 = 7.2 / x
Cross multiplying, we have:
4.2 * x = 1.4 * 7.2
Simplifying, we get:
4.2x = 10.08
Dividing both sides by 4.2, we find:
x = 10.08 / 4.2 ≈ 2.4
So, the larger side of the similar triangle is approximately 2.4 inches.
Therefore, the lengths of the other two sides of the similar triangle are:
The smaller side length is 1.4 inches and the larger side length is 2.4 inches.