Question

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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=(-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.