State which of the following are triangle
b AB = 10 cm ; BC =20 cm ; AC = 7 cm
Answers
Answer
Both are triangle because
sum of any two side > third sidenation:
Answer:
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In a right angled triangle ABC, AB= 10
3
cm and BC=20 cm, ∠A=90
∘
. An equilateral triangle ABD is constructed with base AB and with vertex D at a maximum possible distance from C. Find the length of CD
Medium
Solution
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Correct option is A)
Two equilateral triangles can be termed with the base AB.
But vertex D should be at maximum distance from C.
Therefore, triangle ABD will be preferred.
Now,ΔABD is equilateral triangle.
∴AB=BD=AD=10
3
cm
In right ΔABC
(BC)
2
=(AB)
2
+(AC)
2
(20)
2
=(10
3
)
2
+(AC)
2
(AC)
2
=400−300
AC=10
In ΔACD,∠CAD=90
0
+60
0
=150
0
cos∠CAD=
2(AD)(AC)
(AD)
2
+(AC)
2
−(CD)
2
[∵cosC=
2ab
a
2
+b
2
−c
2
]
cos
6
5π
=
2(10
3
)(10)
10
3
2
+10
2
−CD
2
−
2
3
=
200
3
300+100−(CD)
2
−300=400−(CD)
2
(CD)
2
=700
CD=10
7
cm