Q. 1 B5.0( 1 Vote )
Find the unknown values in each of the following figures. All lengths are given in centimeters. (All measures are not in scale)
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
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