Enter your answer and show all the steps that you use to solve this problem in the space provided. The two triangles above are similar. A. Find X using the ratio of the sides 12 CM + 16 cm. X over 20 equals 12/16. Show your work. B. Find X using the ratio of the side 6 cm and 8 cm. Show your work. C. Explain why the answers to A&B should be the same.
Please help.
Answer:
Part a) x=15cm
Part b) x=15cm
Part c) The answers are the same because the triangles are similar, therefore the ratio of their corresponding sides are equal
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of their corresponding sides are equal and is called the scale factor
Part a) Find x using the ratio of the sides 12 cm and 16 cm
so
12/16 = x/20
3/4 = x/20
The ratio of their corresponding sides is called the scale factor and in this problem is equal to 3/4.
solve for x
x = 20 * 3/4
x = 15 cm
Part b) Find x using the ratio of the sides 6 cm and 8 cm
so
6/8 = x/20
3/4 = x/20
Observe that the scale factor is equal to 3/4
solve for x
x = 20 * 3/4
x = 15 cm
Part c) The answers are the same because the triangles are similar, therefore the ratio of their corresponding sides are equal
Sorry if it doesn't make since.
12/16 = x/20
3/4 = x/20
15/20 = x/20
x = 15
man you just made me dumber
A. To find X using the ratio of the sides 12 cm + 16 cm, we can set up a proportion. The sides of the triangles are in the ratio of 12/16. Let's represent X as the length of the corresponding side in the larger triangle and set up the equation:
X / 20 = 12 / 16
To solve this proportion, we can cross-multiply and then solve for X. Cross-multiplying gives us:
16X = 12 * 20
Simplifying the right side:
16X = 240
Dividing both sides by 16:
X = 240 / 16
X = 15 cm
Therefore, the length of the corresponding side in the larger triangle, X, is 15 cm.
B. To find X using the ratio of the sides 6 cm and 8 cm, we can follow the same process. The sides of the triangles are in the ratio of 6/8. Let's represent X as the length of the corresponding side in the larger triangle and set up the equation:
X / 20 = 6 / 8
Cross-multiplying:
8X = 6 * 20
Simplifying:
8X = 120
Dividing by 8:
X = 120 / 8
X = 15 cm
Therefore, the length of the corresponding side in the larger triangle, X, is also 15 cm.
C. The answers to A and B should be the same because both proportions represent the same similarity ratio between the sides of the two triangles. In both cases, the ratio is 3/4. When the ratio is the same, the corresponding sides of similar triangles are always proportional, which means the lengths of the corresponding sides in the larger triangle will be the same regardless of the specific values used in the proportion. In this case, the length of X is 15 cm in both scenarios because the ratio of the sides is the same.