MNT ~ QRS. Length of altitude drawn from point T is 5 and length of altitude drawn from point S is 9. Find the ratio A( MNT) /A( QRS) .

Given MNT ~ QRS
TMN SQR [corresponding angles of similar triangles]
Construction:
Draw altitude from T to MN meeting at L.
Draw altitude from S to QR meeting at P.
TLM = SPQ = 90˚
In MLT and QPS
TMN SQR
TLM SPQ
MLT ~ QPS [AA test of similarity]
MT/QS = TL/SP
MT/QS = 5/9
MNT ~ QRS [Given]
A( MNT) /A( QRS) = MT²/QS² [Theorem of areas of similar triangles]
A( MNT) /A( QRS) = 5²/9²
A( MNT) /A( QRS) = 25/81
Hence A( MNT):A( QRS) = 25:81