Natalia constructed a right triangle with two side lengths measuring 3 and 5 units. She constructed a second right triangle similar to the first one, with the two corresponding sides measuring 5.1 and x units in length, respectively.



What is the missing length, x, of the second triangle?

since the ratio of the sides remains the same,

x/5 = 5.1/3

8.5

To find the missing length, x, of the second triangle, we can use the property of similar triangles. Similar triangles have corresponding angles that are congruent and corresponding sides that are proportional.

Since the first triangle has side lengths measuring 3 and 5 units, we can set up a proportion to find the corresponding side lengths of the second triangle.

Let's denote the length of the missing side in the second triangle as x. We can set up the following proportion:

(5.1 / 5) = (x / 3)

To solve for x, we can cross-multiply and then divide:

5.1 * 3 = 5 * x

15.3 = 5x

Dividing both sides by 5, we get:

15.3 / 5 = x

x ≈ 3.06

Therefore, the missing length, x, of the second triangle is approximately 3.06 units.