Question

Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar right triangles. Triangle 1 has side length 12, hypotenuse 15, and blank side. Triangle 2 has side length 4, hypotenuse 5, and blank side. a. StartFraction 4 Over 15 EndFraction = StartFraction 5 Over 12 EndFraction = StartFraction 4 Over 15 EndFraction b. StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction c. StartFraction 4 Over 12 EndFraction = StartFraction 5 Over 15 EndFraction = StartFraction 1 Over 3 EndFraction d. StartFraction 5 Over 4 EndFraction = StartFraction 15 Over 12 EndFraction = StartFraction 5 Over 4 EndFraction

Answer 1

The correct ratio of corresponding sides for the similar triangles, reduced to lowest terms, is 4/5. This represents the relationship between the known side lengths and hypotenuse of Triangle 1 and Triangle 2, which is option b.

Step-by-step explanation:

To find the ratio of corresponding sides for the similar triangles, we compare the lengths of known sides. Since we are given the side lengths and the hypotenuse for both triangles, we can write the ratios and then reduce them to their simplest form. It's important to compare the corresponding sides of both triangles accurately.

In this case, Triangle 1 has a side length of 12 and a hypotenuse of 15. Triangle 2 has a side length of 4 and a hypotenuse of 5. Setting up the ratio of corresponding sides (side to hypotenuse) gives us:

• T1: 12 / 15 (can be reduced to 4 / 5)
• T2: 4 / 5 (already in simplest form)

Note: It is incorrect to compare a side length from one triangle to the hypotenuse of another triangle as corresponding sides, which would have been done in option a. The ratios must compare the same types of sides (e.g., side-to-side, hypotenuse-to-hypotenuse).

The correct ratio in the simplest form is represented by option b: 4 / 5. This means for every 4 units of length in one triangle, there are 5 units of length in the other, maintaining the proportionality of their sizes.

Answer 2

Step-by-step explanation: To find the ratio of corresponding sides for the two similar triangles, we need to match up the corresponding sides of the triangles and write the ratios of their lengths.

For Triangle 1, we have:

Side length = 12

Hypotenuse = 15

We can use the Pythagorean theorem to find the length of the blank side:

(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2

(Blank side)^2 = 15^2 - 12^2

(Blank side)^2 = 225 - 144

(Blank side)^2 = 81

Blank side = 9

So, for Triangle 1, we have the following ratios:

Side length : Hypotenuse = 12 : 15

Side length : Blank side = 12 : 9

Hypotenuse : Blank side = 15 : 9

For Triangle 2, we have:

Side length = 4

Hypotenuse = 5

We can use the Pythagorean theorem to find the length of the blank side:

(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2

(Blank side)^2 = 5^2 - 4^2

(Blank side)^2 = 25 - 16

(Blank side)^2 = 9

Blank side = 3

So, for Triangle 2, we have the following ratios:

Side length : Hypotenuse = 4 : 5

Side length : Blank side = 4 : 3

Hypotenuse : Blank side = 5 : 3

Therefore, the ratio of corresponding sides for the two similar triangles is:

Side length : Side length = 12 : 4 = 3 : 1

Hypotenuse : Hypotenuse = 15 : 5 = 3 : 1

Blank side : Blank side = 9 : 3 = 3 : 1

Reducing each ratio to lowest terms, we get:

Side length : Side length = 3 : 1

Hypotenuse : Hypotenuse = 3 : 1

Blank side : Blank side = 3 : 1

So the correct answer is (b) StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction.