Question

∆MNT ~ ∆QRS. Length of altitude drawn from point T is 5 and length of altitude drawn from point S is 9. Find the ratio \(\frac{A(\Delta MNT)}{A(\Delta QRS)}\)

Answer 1

∆MNT- ∆QRS [Given]

∴ \(\angle\)M ≅ \(\angle\)Q (i) [Corresponding angles of similar triangles]

In ∆MLT and ∆QPS,

\(\angle\)M ≅ \(\angle\)Q [From (i)]

\(\angle\)MLT ≅ \(\angle\)QPS [Each angle is of measure 90°]

∴ ∆MLT ~ ∆QPS [AA test of similarity]