If fig.PA,QB and RC are each perpendicular to AC.If x=8cm and z=6cm,then y is equal to..
(a) 56/7 (b) 7/56 (c) 25/7 (d) 24/7.
Answers
Answer:
24/7
Step-by-step explanation:
answer is 24/7 explain khud karlo
- 24/7 .
Given :- fig.PA,QB and RC are each perpendicular to AC . x = 8cm and z = 6cm .
To Find :- Value of y ?
(a) 56/7 (b) 7/56 (c) 25/7 (d) 24/7.
Solution :-
In ∆CQB and ∆CPA
→ ∠QCB = ∠PCA { Common }
→ ∠QBC = ∠PAC { since PA ⊥ AC and QB ⊥ AC, each 90° }
So,
→ ∆CQB ~ ∆CPA { By AA similarity. }
then,
→ CB/CA = QB/PA { When two ∆'s are similar their corresponding sides are in same ratio. }
→ CB/CA = QB/8
→ CB = (QB/8)•CA ---------- Eqn.(1)
Similarly,
In ∆AQB and ∆ARC
→ ∠QAB = ∠RAC { Common }
→ ∠ABQ = ∠ACR { since RC ⊥ AC and QB ⊥ AC, each 90° }
So,
→ ∆AQB ~ ∆ARC { By AA similarity. }
then,
→ AB/AC = QB/RC { When two ∆'s are similar their corresponding sides are in same ratio. }
→ AB/AC = QB/6
→ AB = (QB/6)•AC ---------- Eqn.(2)
adding Eqn.(1) and Eqn.(2) we get,
→ CB + AB = {(QB/8)•CA} + {(QB/6)•AC}
→ CB + AB = AC[(QB/8) + (QB/6)]
→ AC = AC[(QB/8) + (QB/6)]
→ 1 = (QB/8) + (QB/6)
→ 1 = (3QB + 4QB)/24
→ 24 = 7QB
→ QB = (24/7)
→ y = (24/7) cm (Ans.)
Shortcut :-
When three lines are perpendicular to one line,
→ 1/y = 1/x + 1/z
→ 1/y = 1/8 + 1/6
→ 1/y = (3 + 4)/24
→ 1/y = (7/24)
→ y = (24/7) (Ans.)
Hence, Length of y is equal to (24/7) cm .
Learn more :-
In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .
brainly.in/question/32333207
