Question

Find the length of ST, if ΔPQR ∼ ΔPST.

Options

• 7.2 cm

• 7 cm

• 8 cm

• 9 cm

Answer 1

7.2 cm

Explanation:

Given: ΔPQR ∼ ΔPST

∴ `(PQ)/(PS) = (QR)/(ST)`  ......[Corresponding parts of similar triangles]

⇒ `(PS + SQ)/(PS) = (QR)/(ST)`

⇒ `(4 + 6)/4 = 18/(ST)`

⇒ `10/4 = 18/(ST)`

10 × ST = 18 × 4

ST = `72/10` = 7.2 cm

Thus, the length of ST is 7.2 cm.