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If in a triangle, angles are in the ratio 1:1:2 and the length of its longest side is L cm, then what is the perimeter of the triangle?
Let the angles of the triangle are A, A and 2A respectively.
4A = 180 0 ...........................(Angle sum property)
A = 45 0
Angles are 45 0 , 45 0 and 90 0 respectively.
It is a right angle isosceles tringle,
Other 2 sides = L/ (√2)
Perimeter = L + (L/√2) + (L/√2)
= L +L√2 = L (1 +√2) cm.
If d is the side of a triangle and 2-(1/d) - (15/d 2 ) = 0, then what is the value of ((d 4 -4)/(d 3 -3))?
2-(1/d) - (15/d 2 ) = 0
2d 2 -d - 15 = 0
(d-3) x (2d +5) = 0
d = 3 or d = - 5/2
But 'd' is the side of a triangle .
so d will be positive .
((d 4 -4)/(d 3 -3)) = (81-4)/(27-3) = (77/24)
In a trapezium MNOP, MN || OP, diagonal PN and OM are intersect at point A and ratio of area of △MNA to the area of △OPA is 4 : 9, then find OP : MN.
In △MNA and △OPA, ∠MAN = ∠PAO (∴ Opposite angles)
∠MNA = ∠APO (∴ Alternate angles)
∠NMA = ∠AOP (∴ Alternate angles)
So, △MNA and △OPA are similar.
In similar triangle, Ratio of their area = Square of ratio of their corresponding sides
=> Area of △MNA : Area of △OPA = (MN) 2 : (OP) 2
=> 4 : 9 = (MN) 2 : (OP) 2
=> MN : OP = 2 : 3
=> OP : MN = 3 : 2
If 4x 2 + 16y 2 - 12x - 40y + 34 = 0, then find the value of x/y.
4x 2 + 16y 2 - 12x - 40y + 34= 0
(4x 2 - 12x + 9) + (16y 2 - 40y + 25) = 0
(2x - 3) 2 + (4y - 5) 2 = 0
2x - 3 = 0 => x = 3/2
4y - 5 = 0 => y = 5/4
(x/y) = x * (1/y) = (3/2) * (4/5) = 6/5
A chord of length 14 cm is drawn perpendicular to the diameter of the circle having radius 25 cm. Find the distance of point of intersection of chord and diameter from the centre of circle.
In triangle OPA, OA = 25 cm (Radius)
AP = AB/2 = 14/2 = 7cm
OP = √(OA 2 - AP 2 ) = √(25 2 - 7 2 ) = √(625 - 49) = √576 = 24 cm
Hence, distance of point of intersection of chord and diameter from the centre of circle = 24 cm
If P is m% more than Q, then Q is?
As P is m% more than Q
P = Q + ((m/100) x Q)
P = ((100 +m)/100) x Q
Q = (100/ (100 +m)) x P
If 2x 3 + x 2 -mx -4 is divided by x -2, then remainder is zero, then what is the value of m?
When 2x 3 + x 2 -mx -4 is divided by x -2 and remainder is zero, it means
For x = 2, 2x 3 + x 2 -mx -4 = 0
2 x (2) 3 +(2) 2 - (2m) -4 =0
-2m =-16
m = 8
How many numbers from 1 to 901 are there which are divisible by either 3 or 9 but not by both?
Total numbers from 1 to 901 which are divisible by 3 = (900/3) = 300
Total numbers from 1 to 901 which are divisible by 9 = (900/9) = 100
All numbers which are divisible by 9 are divisible by 3 also
Total numbers divisible by either 3 or 9 but not by both = 300-100 = 200
Directions For Questions
Following table shows number of T-20 matches played, runs scored,50s and 100s by 4 Indian batsmen in a year.
...view full instructions
What is the average of the total number of runs scored by all 4 batsmen together?
Required average = (900 +840 +1050 +450)/4 = 3240/4 = 810
What is the difference between average runs per match scored by Virat and average runs per match scored by Suresh?
Average runs per match scored by Virat = (900/16) = (225/4)
Average runs per match scored by Suresh = (450/12) = (150/4)
Required difference = (225/4) - (150/4) = (75/4) = 18.75
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