Question

Help? Show work! Triangle PQR ≅ Triangle XYZ PQ = 3a + 4 and XY = 5a – 12. Find a and PQ.

Answer 1

Given:

$\Delta PQR\cong \Delta XYZ$

$PQ=3a+4$

$XY=5a-12$

To find:

The value of a and PQ.

Solution:

We have,

$\Delta PQR\cong \Delta XYZ$

$PQ\cong XY$                            (CPCTC)

So,

$PQ=XY$

$3a+4=5a-12$

Isolating variable terms, we get

$3a-5a=-4-12$

$-2a=-16$

Divide both sides by -2.

$a=\dfrac{-16}{-2}$

$a=8$

Now,

$PQ=3a+4$

$PQ=3(8)+4$

$PQ=24+4$

$PQ=28$

Therefore, the value of a is 8 and the value of PQ is 28.