Question

In adjoining figure
seg PS perpendicular to seg RQ seg QT perpendicular to seg PR.
If RQ = 6, PS = 6 and PR = 12,
then find QT.​

Answer 1

Answer:

Given:

PS ⊥ RQ

QT ⊥ PR

RQ = 6, PS = 6 and PR = 12

With base PR and height QT,

A(△PQR)=½×PR×QT

With base QR and height PS,

A(△PQR)=½×QR×PS

∴A(△PQR)/A(△PQR)=½×PR×QT/½×QR×PS

⇒1=PR×QT/QR×PS

⇒PR×QT=QR×PS

⇒QT=QR×PS/PR

=6×6/12

=3

Hence, the measure of side QT is 3 units.