Subject :IMO Class : Class 9
State 'T' for true and 'F' for false.
(i) A triangle whose sides measure 8 cm, 4 cm and 12 cm can be possible.
(ii) It is possible to construct an angle of 67.5° using ruler and compass only.
(iii) It is possible to construct a ∆XYZ in which ∠X = 60°, ∠ Y = 100° and ∠ Z = 20°.
(i) (ii) (iii)
A TFT
B FFF
C FTT
D TTF
This given answer seems to be wrong. Can someone kindly check?
Ans 1:
Class : Class 9
C option is correct......as the first is false and rest are true.
Ans 2:
Class : Class 9
Yes it is correct
Ans 3:
Class : Class 10
The answer is (C) --- F,T,T. Here's why:The first one is false anyway, as the '12' side is equal to (not less than, as must be) the sum of the other two '4' and '8' sides.The second one is TRUE (not false!) as I can easily construct a 90^ angle and 45^ angle with ruler and compass; and simply bisect that in-between angle to get a 67.5 angle.Even the third one is TRUE (not false) as construction of a triangle allows using a protractor for angles (that's how R.D.Sharma and my teacher do it) and ANY such triangle can be constructed. In short, my answer is correct. I marked the same, but the olympiad trainer says that it is (B) --- all are false.
Ans 4:
Class : Class 10
Actually, the answer should be FTF which is not given in the options. Considering statement 1, the sides of the triangle are 4cm, 8cm, and 12cm. But according to inequalities of triangles, sum of any to sides of a triangle is greater than the third side. But 4+8=12; i.e. sum of the two sides is equal to the third side. So statement 1 is FALSE. Considering statement 2, it is possible to construct an angle of 67.5 only using a ruler and compass. Taking statement 3, without a base, we can't construct a triangle.