The two triangles above are similar
(The triangle to the right show the numbers 6,12, and x. The triangle to the left has the numbers 20,16 and 8.)
A. Find x using the ratios of the sides 12 cm and 6 cm: x/20=12/16
B. Find x using the ratios of the sides 6 cm and 8 cm
C. Explain why the answers to A and B should be the same.
I don’t understand this question and any help would be very appreciated.
We can not see your drawing
if a,b,c is similar to A, B, C then
a/b = A/B
a/c= A/C
b/c = B/C
etc, etc, etc
I would assume that you wrote the sides in the proper correspondence, that is if
6:12:x = 20,16,8
then the angle opposite 6 would be equal to the angle opposite 20 etc
then 6/20 = 12/16, which is not the case
relist the sides in their corrct sequence
To understand this question, we need to understand what it means for two triangles to be similar. Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are proportional.
Let's solve this step by step:
A. Find x using the ratios of the sides 12 cm and 6 cm: x/20 = 12/16
To solve for x, we will set up a proportion using the given ratios:
x/20 = 12/16
Cross-multiplying, we get:
16x = 12 * 20
Simplifying:
16x = 240
Dividing both sides of the equation by 16:
x = 240/16
x = 15
Therefore, for the given sides 12 cm and 6 cm, the value of x is 15 cm.
B. Find x using the ratios of the sides 6 cm and 8 cm:
To find x using the ratios of the sides 6 cm and 8 cm, we set up a proportion:
6/x = 8/20
Cross-multiplying:
8x = 6 * 20
Simplifying:
8x = 120
Dividing both sides of the equation by 8:
x = 120/8
x = 15
Therefore, for the given sides 6 cm and 8 cm, the value of x is also 15 cm.
C. Explain why the answers to A and B should be the same:
The answers to A and B should be the same because both solutions are finding the value of x using the concept of similarity. Since the two triangles are similar, their corresponding sides must be proportional. In other words, the ratios of corresponding sides should be equal.
In case A, we set up the proportion using the ratio of the sides 12 cm and 6 cm. In case B, we set up the proportion using the ratio of the sides 6 cm and 8 cm. However, in both cases, the resulting proportion is the same, and therefore the value of x is also the same - 15 cm.
This shows that regardless of which pair of corresponding sides we choose, the similarity property guarantees that the answers will be the same.