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04 Oct 2021, 01:30
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In a parallelogram, the ratio of the two adjacent sides is 1:2. If the area of the parallelogram is \(36√2\) square unit and the angle between the two sides is \(45°\), what is the area, in square unit, of the rectangle whose smaller side is equal to the smaller side of the parallelogram and the larger side is equal to the larger side of the parallelogram?
A 36
B \(36\sqrt{2}\)
C 72
D 96
E 144
A 36
B \(36\sqrt{2}\)
C 72
D 96
E 144
asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
04 Oct 2021, 06:09
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Area of ||gm = ab sin θ ( where a and b are the length of sides of ||gm)
Given area = 36√2
ab sin 45 = 36√2( given that the angle between two sides is 45)
ab = 36*2 = 72
Also given that the sides are in the ratio of 2:1
So if the longer side = 2x then shorter side = x
2x^2 = 72
x^2 =36
x = 6
Shorter side =6
Longer side =12
Area of rectangle = 6*12 = 72
IMO C
Given area = 36√2
ab sin 45 = 36√2( given that the angle between two sides is 45)
ab = 36*2 = 72
Also given that the sides are in the ratio of 2:1
So if the longer side = 2x then shorter side = x
2x^2 = 72
x^2 =36
x = 6
Shorter side =6
Longer side =12
Area of rectangle = 6*12 = 72
IMO C
04 Oct 2021, 10:32
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area of parallelogram = base * height
In question, it was given side are in the ratio 1:2 and angle between them is 45degree.
so sides will be in the form a and 2a.
If we draw perpendicular, consideration base a units, we will have a right angle isosceles triangles( Angle are 45 degree).
According to Pythagorus theorem, we can find height = square root( 2) * a.
a*square root (2) *a = 36*square root (2)
a=6.
rectangle area = 6*12 = 72.
In question, it was given side are in the ratio 1:2 and angle between them is 45degree.
so sides will be in the form a and 2a.
If we draw perpendicular, consideration base a units, we will have a right angle isosceles triangles( Angle are 45 degree).
According to Pythagorus theorem, we can find height = square root( 2) * a.
a*square root (2) *a = 36*square root (2)
a=6.
rectangle area = 6*12 = 72.
