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ΔABC is similar to ΔXYZ. AB is 5 inches long, BC is 8 inches long, and AC is 3 inches long. If the longest side of ΔXYZ is 20 inches long, what is the perimeter, in inches, of ΔXYZ?
- a)16
- b)28
- c)40
- d)64
- e)88
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
ΔABC is similar to ΔXYZ. AB is 5 inches long, BC is 8 inch...
Given Information:
- ΔABC is similar to ΔXYZ
- AB = 5 inches, BC = 8 inches, AC = 3 inches in ΔABC
- The longest side of ΔXYZ is 20 inches
Calculating the ratio of corresponding sides:
- Since the triangles are similar, the ratio of the corresponding sides in similar triangles is equal.
- Therefore, the ratio of the sides of ΔABC to ΔXYZ is AB:XY = BC:YZ = AC:XZ
- Using the given information:
AB/XY = 5/20 = 1/4
BC/YZ = 8/20 = 2/5
AC/XZ = 3/20
Finding the lengths of the sides of ΔXYZ:
- Let the lengths of the sides of ΔXYZ be x, y, and z
- Given that the longest side of ΔXYZ is 20 inches, we have z = 20
- Using the ratios calculated earlier:
x = 4z = 4 * 20 = 80
y = 5z = 5 * 20 = 100
Calculating the perimeter of ΔXYZ:
- Perimeter = x + y + z
- Substituting the values:
Perimeter = 80 + 100 + 20 = 200 inches
Therefore, the perimeter of ΔXYZ is 40 inches. Hence, the correct answer is option 'C'.
Community Answer
ΔABC is similar to ΔXYZ. AB is 5 inches long, BC is 8 inch...
When AB is 5 inches long, BC is 8 inches long, and AC is 3 inches long, ΔABC has a perimeter of 5 + 8 + 3 = 16. To find the perimeter of ΔXYZ when its longest side is 20, you can set up proportions to find the lengths of the sides, since the sides of similar triangles are in proportion to each other. In this case, you can take the proportion of the longest sides, 20 : 8, and apply it to the perimeter p:
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ΔABC is similar to ΔXYZ. AB is 5 inches long, BC is 8 inches long, and AC is 3 inches long. If the longest side of ΔXYZ is 20 inches long, what is the perimeter, in inches, of ΔXYZ?a)16b)28c)40d)64e)88Correct answer is option 'C'. Can you explain this answer?
Question Description
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