From a given perimeter how many triangles with integral sides are possible?
We can solve this question within seconds with the help of a tips and tricks. Generally there are two cases for these type of questions.
Scenario 1:
When Perimeter is odd
Scenario 2:
When perimeter is even
Scenario 1 – Details
Solution – In this case, total number of triangles will be the nearest integer to P2/48
Scenario 2 – Details
Solution – In this case, total number of triangles will be the nearest integer to
(a) π/3
(b) πr2/3
(c) πr2/4
(d) 2πr/4r
Ans: a
Sol:
OD2 = OA2+ AD2
(2r)2 = r2 + AD2
Thus PQ, which is also the side of square, is equal to r√3. The area of square becomes: 3r2
Hence the ratio of the area of circle to square is:
Correct Option (A)
Q2: If in a triangle ABC, then what can be said about the triangle ?
(a) Right angled triangle
(b) Isosceles triangle
(c) Equilateral triangle
(d) Nothing can be inferred
Ans: c
Sol:
From the sine rule of triangle we know,
Therefore, a = k(sin A), b = k(Sin B) and c = k(Sin C)
Hence, we can rewrite,
or Cot A= Cot B= Cot C
A = B = C, Hence the triangle is equal.
Correct Option (C)
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