Question

In PQR triangle , PQ=PR=13. If the length of the altitude drawn from Q perpendicular to side PR is 12 what is the perimeter of PQR?

Answer 1

Given Q is perpendicular to PR in PQR! Let's consider that altitude from Q intersects PR at S!

Then in QSP!

(PQ)² = (PS)² + (QS)²

=> PS = 5!

=> RS = 8!

In QSR

(QR)² = (QS)² + (SR)²

=> QR = 4√13

Perimeter = 13 + 13 + 4√13 = 26 + 4√13!

Hope it helps!