Question

Triangle PQR \cong Triangle XYZ
PQ = 3a + 4 and XY = 5a – 12. Find a and PQ.

Answer 1

Answer:

Step-by-step explanation:

PQ = 3a + 4 ---- (1)

XY = 5a – 12 ------- (2)

As Triangle PQR is congruent to Triangle XYZ.

By the theoram of congruent triangles,

PQ congruent to XY

Substituting PQ with XY in equation (1), we get

XY=3a+4 ----- (3)

Comparing (3) and (2), we get

3a+4=5a-12

12+4=5a-3a

16=2a

a=8

Subsituting value of a in equation (1) to get value of PQ

PQ=3a+4

=3×8+4

=24+4

=28.

Hence a=4 and PQ=28