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Roman55 [17]
3 years ago
14

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

Mathematics
1 answer:
Ivenika [448]3 years ago
5 0

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.

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