Dear Jiskha Tutors,
Please help me Understand this. Thank you,
Two triangles are shown. The first triangle has sides x, 6 cm, and 12 cm, and the second triangle has corresponding sides 20 cm, 8 cm, and 16 cm.
The two triangles above are similar.
A. Find X using the ratio of the sides 12 cm and 16 cm: x/20=12/16. Show your work.
B. Find x using the ratio of the sides 6 cm and 8 cm. Show your work.
C.Explain why the answers to (a) and (b) should be the same.
Don't have to tell me the answer, just explain it.
~Thank you,
Foxfrost, 7th grade.
since corresponding sides are in the same ratio,
x/20 = 6/8 = 12/16
They explained it already, and even gave the proportion to solve
I don't wet it :"<
A. To find x using the ratio of the sides 12 cm and 16 cm, we have the proportion:
x / 20 = 12 / 16
To solve for x, we can cross-multiply and then simplify:
16x = 12 * 20
16x = 240
Now, divide both sides by 16 to isolate x:
x = 240 / 16
x = 15 cm
Therefore, x is equal to 15 cm.
B. Similarly, to find x using the ratio of the sides 6 cm and 8 cm, we have the proportion:
x / 20 = 6 / 8
Cross-multiply and simplify:
8x = 6 * 20
8x = 120
Divide both sides by 8 to solve for x:
x = 120 / 8
x = 15 cm
So, the value of x is also 15 cm in this case.
C. The reason the answers to parts (a) and (b) should be the same is that both triangles are similar. Similar triangles have proportional side lengths. In this case, the sides of the first triangle (x, 6 cm, and 12 cm) are proportional to the corresponding sides of the second triangle (20 cm, 8 cm, and 16 cm).
Since the triangles are similar, the ratios of corresponding side lengths are equal. Therefore, the ratios of 12 cm to 16 cm and 6 cm to 8 cm are equal, and both ratios are equal to x cm to 20 cm.
This means that x is the same value in both ratios. So, when we solve for x using either ratio, we should get the same value, as we did in parts (a) and (b) where x was found to be 15 cm in both cases.
Dear Foxfrost,
To find the value of x in each scenario, we need to use the concept of similarity between the two triangles. Similar triangles have the same shape but can be different in size.
A. Finding x using the ratio of the sides 12 cm and 16 cm:
We have the ratio of x to 20 cm given as x/20 = 12/16.
We can cross multiply to solve for x:
16 * x = 12 * 20
16x = 240
x = 15
So, the value of x in this case is 15 cm.
B. Finding x using the ratio of the sides 6 cm and 8 cm:
We don't have the value of x directly, but we can set up a similar proportion using the ratio of the sides.
The ratio is x to 20 cm, so we can write x/20 = 6/8.
Cross multiplying, we get:
8 * x = 6 * 20
8x = 120
x = 15
So, the value of x in this case is also 15 cm.
C. Explaining why the answers to (a) and (b) should be the same:
In both scenarios, we are comparing the lengths of the sides in the first triangle to the corresponding lengths in the second triangle. Since the triangles are similar, all corresponding sides have the same ratio. Therefore, the value of x, which corresponds to the unknown side length in each case, should be the same.
I hope this explanation helps you understand how to find the value of x in each scenario and why the answers to (a) and (b) should be the same.
Best,
Explain Bot