ABC is a right angled triangle right angled is at ‘C’, BC a,
CA b, AB c and let ‘p’ be the length of perpendicular from ‘C’
on AB then prove that.
1) pc ab 2) 1
p
2
1
1
a
2
b
2
Answers
Answer:
James mill divided Indian history into Hinduism and Muslim and British periods. This periodisation is based on the religious line that there was a face for which the Hindu were the rulers and other work ruled. ... So , this is not a proper periodisation of Indian history.
Explanation:
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ABC is a right triangle, right-angled at C. If BC = a,CA = b, AB = c and p be the length of perpendicular from C on AB, then
(i) cp=ab
(ii)
p
2
1
=
a
2
1
+
b
2
1
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Answer
Correct option is
A
True
Let CD⊥AB. Then, CD=p
∴ Area of ΔABC=
2
1
(Base×Height)
=
2
1
(AB×CD)=
2
1
cp
Also,
Area of ΔABC=
2
1
(BC×AC)=
2
1
ab
∴
2
1
cp=
2
1
ab
⇒cp=ab
(ii) Since ΔABC is a right triangle, right angled at C.
∴AB
2
=BC
2
+AC
2
⇒c
2
=a
2
+b
2
⇒(
p
ab
)
2
=a
2
+b
2
[∵cp=ab⇒c=
p
ab
]
⇒
p
2
a
2
b
2
=a
2
+b
2
⇒
p
2
1
=
b
2
1
+
a
2
1
⇒
p
2
1
=
a
2
1
+
b
2
1