Q1) There are three equal circles of unit radii touching each other. Find the area of triangle circumscribing these circles? a) v3 (v3 +1)2 b) (v3 +1)2 c) v3 (v3 +1) d) none of these What would be the area of remaining portion if he same three circles are circumscribed by another circle? a) π(2/v3 +1)2 b) π(2/v3 +1)2 - 3π c) (3/v2 +1)2 π - 3π d) (1/v3 +1)2 π - 3π Q2) The angles of a triangle are in the ratio of 4:1:1, then the ratio of largest side to perimeter is: a)2/3 b)1/(2+v3) c) v3/(2+v3) d) 2/(1+v3) Q3) The sides of a triangle are in the ratio of 1:2:4, then the ratio of altitudes drawn onto these sides is: a) 4:2:1 b) 1:2:4 c) 1:4:16 d) none of these Q4) The longest side of a triangle is 20 & another side has length 10.It's area is 80.What is the exact length of third side? a) v260 b) v250 c) v240 d) v270 |
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The answer is a. √ 3 (√3 +1)2
hi neel,
i think thr is a mistake in options of Q2. bcoz da answr according to me is 1/(1 + √3).
Pain is absolute but... Suffering is OPTIONAL !
n/a
hi frnds,
answr to Q4. is √240
it can b solved by applying 2 formulae:-
i). cosθ = (a² + b² - c²)/2ab
ii). area of triangle = (absinθ)/ 2
n i hope u people remember..... sin²θ + cos²θ = 1
Pain is absolute but... Suffering is OPTIONAL !
n/a
kan sumone explain Q1 with help of a figure??? where r u RAVI.......???
& ans to Q4) is v260.. The suggested method is right bt calculation is wrong...
Thanx :-)
The angles of a triangle are in the ratio of 4:1:1, then the ratio of largest side to perimeter is:
The angles of the triangle are 120 : 30 : 30
We Know a/ SinA = b/ SinB = c/ SinC = K
a = K SinA = K Sin120 = √ 3/2
b = K SinB = K Sin30 = 1/2
c = K SinC = K Sin30 = 1/2
the ratio of largest side to perimeter is √ 3/2 / (√ 3/2 + 1) = √ 3/ (√ 3 + 2) (ans c)
radius of the circle = 1
=> ab = bc = ca = 2
So bP = √ 3
and op is 1/3 rd of bp
= > op = 1/ √ 3
and OQ = 1 + 1/ √ 3 = (√ 3 + 1)/√ 3 -------------(1)
=> BQ = √3/2 a and OQ is 1/3rd of that
=> OQ = a/2√3 -----------------------(2)
From Eq (1) and Eq(2)
a = 2 ( √3 + 1)
and area = √3/4 * a2
= √ 3 (√3 +1)2
n/a
The answer should be b> and it is correct.
Correct answer is srt260. Solve it carefully.
Thanx for the solutn NISHIT !!!
:-)
my answers are as follows:
Q1---->first part........(a).......a little tricky bt simple cuz each circles have same radius......apply sinx=p/h and find the altitude of the triangle
Q1---->second part......(d).....construct an inner triangle.......find its inradius frm the formula area= rs......u get the rdius of the bigger circle frm this....proceed to find the answer.
Q2----->(c).....its an isoscles triangle......so the altitude bisects the 120 deg angle......take one side as x or 1and apply sine formula to find the longer side)...proceed to calculate the area and the perimter)
Q3------>(d)........(these are not triangle sides cuz sum of two is not greater than the third)
Q4------>(a).........(find out d altitude frst(area is given)......and then apply pythagoras to find the desired side)
i think my answers are 100 percent correct.....if u face any prob.....plz reply....neways nice questions...
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