Since triangle ABC is congruent to triangle PQR, their corresponding sides are congruent. Thus:
AB = PQ
BC = QR
CA = RP
Using the given information, we can set up the following equations:
AB = PQ
3x + 7 = 2x + 12
x = 5
BC = QR
5y + 11 = y + 59
4y = 48
y = 12
CA = RP
5z - 12 = 2z + 27
3z = 39
z = 13
Therefore, we have found the values of x, y, and z, which are 5, 12, and 13, respectively. We can substitute these values into the given expressions for AB, BC, and CA to find their actual lengths:
AB = 3x + 7 = 3(5) + 7 = 22 cm
BC = 5y + 11 = 5(12) + 11 = 71 cm
CA = 5z - 12 = 5(13) - 12 = 53 cm
Hence, we have found the lengths of the sides of triangle ABC.
Answers & Comments
Answer:
Since triangle ABC is congruent to triangle PQR, their corresponding sides are congruent. Thus:
AB = PQ
BC = QR
CA = RP
Using the given information, we can set up the following equations:
AB = PQ
3x + 7 = 2x + 12
x = 5
BC = QR
5y + 11 = y + 59
4y = 48
y = 12
CA = RP
5z - 12 = 2z + 27
3z = 39
z = 13
Therefore, we have found the values of x, y, and z, which are 5, 12, and 13, respectively. We can substitute these values into the given expressions for AB, BC, and CA to find their actual lengths:
AB = 3x + 7 = 3(5) + 7 = 22 cm
BC = 5y + 11 = 5(12) + 11 = 71 cm
CA = 5z - 12 = 5(13) - 12 = 53 cm
Hence, we have found the lengths of the sides of triangle ABC.