Ina right angle ∆ABC, angle B=90⁰, AC=30 ,AB= 4a & BC= 3a, then the value of a is _______
(A) 6 (B) 12 (C)18 (D) 24
Answers
Step-by-step explanation:
Correct option is
B
5AC
2
Given, △ABC, M is mid point of AB and N is mid point of BC.
In △ABN,
AN
2
=AB
2
+BN
2
(Pythagoras Theorem)
AN
2
=AB
2
+(
2
BC
)
2
....(1)
In △BMC,
MC
2
=BM
2
+BC
2
(Pythagoras Theorem)
MC
2
=BC
2
+(
2
AB
)
2
....(2)
Add (1) and (2),
AN
2
+MC
2
=AB
2
+(
2
BC
)
2
+BC
2
+(
2
AB
)
2
AN
2
+MC
2
=
4
5
AB
2
+
4
5
BC
2
4(AN
2
+MC
2
)=5(AB
2
+BC
2
)
4(AN
2
+MC
2
)=5AC
2
(Pythagoras Theorem in △ABC)
Given :- In a right angle ∆ABC, angle B=90⁰, AC=30 ,AB= 4a & BC= 3a .
To Find :- the value of a is _______
(A) 6
(B) 12
(C)18
(D) 24
Solution :-
since angle B = 90° . side AC which opposite to vertex B is hypotenuse .
so, according to pythagoras theorem,
→ (perpendicular)² + (base)² = (hypotenuse)²
→ (AB)² + (BC)² = (AC)²
→ (4a)² + (3a)² = (30)²
→ 16a² + 9a² = 900
→ 25a² = 900
→ a² = 36
→ a = 6 { Taking positive value .}
Hence, value of a is equal to 6 .
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