Given:
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ=3a+4[/tex]
[tex]XY=5a-12[/tex]
To find:
The value of a and PQ.
Solution:
We have,
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ\cong XY[/tex] (CPCTC)
So,
[tex]PQ=XY[/tex]
[tex]3a+4=5a-12[/tex]
Isolating variable terms, we get
[tex]3a-5a=-4-12[/tex]
[tex]-2a=-16[/tex]
Divide both sides by -2.
[tex]a=\dfrac{-16}{-2}[/tex]
[tex]a=8[/tex]
Now,
[tex]PQ=3a+4[/tex]
[tex]PQ=3(8)+4[/tex]
[tex]PQ=24+4[/tex]
[tex]PQ=28[/tex]
Therefore, the value of a is 8 and the value of PQ is 28.
