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08 Dec 2020, 01:02
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An obtuse triangle is a triangle that has an interior angle whose measure is greater than 90 degrees. John has drawn all obtuse triangles with an area of 20 square inches whose angle measures in degrees are all multiples of 10. How many triangles has he drawn?
(A) 13
(B) 14
(C) 15
(D) 16
(E) more than 16
Are You Up For the Challenge: 700 Level Questions
(A) 13
(B) 14
(C) 15
(D) 16
(E) more than 16
Are You Up For the Challenge: 700 Level Questions
08 Dec 2020, 06:09
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Bunuel
An obtuse triangle is a triangle that has an interior angle whose measure is greater than 90 degrees. John has drawn all obtuse triangles with an area of 20 square inches whose angle measures in degrees are all multiples of 10. How many triangles has he drawn?
(A) 13
(B) 14
(C) 15
(D) 16
(E) more than 16
(A) 13
(B) 14
(C) 15
(D) 16
(E) more than 16
There is no restriction on the length of side, so whatever be the angles, we can always stretch the sides to ensure that we have area of 20 square inches.
So, the question is now - ' How many ways can we make an obtuse triangle with angles multiple of 10?'
Let the obtuse angle be 100.
a) 100 : Other possible angles (40, 40), (30, 50), (20, 60), (10, 70) - 4 different triangles
b) 110 : Other possible angles (40, 30), (20, 50), (10, 60), - 3 different triangles
c) 120 : Other possible angles (30, 30), (20, 40), (10, 50), - 3 different triangles
d) 130 : Other possible angles (20, 30), (10, 40), - 2 different triangles
e) 140 : Other possible angles (20, 20), (10, 30), - 2 different triangles
f) 150 : Other possible angles (20, 10), - 1 different triangle
g) 160 : Other possible angles (10, 10), - 1 different triangle
Total 4+3+3+2+2+1+1=16
D
02 May 2022, 21:51
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Why can't the obtuse angle change the position and it will be a different triangle - say Triangle 1 has angle A is 100 and B, C are 40, 40. Then in next example with same set of angles, Triangle 2 may have Angle B as 100 and A, C as 40, 40 - it will make the difference when the triangle is drawn in coordinate plane and hence the triangles 1 and 2 will be different but with same angle measures overall.
