Find the unknown values in each of the following figures. All lengths are given in centimeters. (All measures are not in scale)

Question

Philoid · Accepted Answer

We need to find x, y and z. i.e. FG and EF respectively.

Now,

In ΔHFG and ΔHBC

∠HFG = ∠HBC by corresponding angles (DG∥BC)

∠HGF = ∠HCB by corresponding angles (FG∥BC)

∴ ΔHFG ∼ ΔHBC

(∵ ΔHFG ∼ ΔHBC)

⇒ x = 3.6 cm

Now,

In ΔFHG and ΔFBD

∠DFB = ∠HFG by vertically opposite angles

∠FDB = ∠FGH by alternate angles (DB∥AC)

∴ ΔFHG ∼ ΔFBD

⇒ 6×3.6 = 12 + 4y (∵ x=3.6)

⇒ y = 2.4 cm

Now,

In ΔAEG and ΔABC

∠AEG = ∠ABC by corresponding angles (EG∥BC)

∠AGE = ∠ACB by corresponding angles (EG∥BC)

∴ ΔAEG ∼ ΔABC

(∵ ΔAEG ∼ ΔABC)

(∵ x=3.6 and y=2.4)

⇒ z = 10 cm