In a parallelogram, the ratio of the two adjacent sides is 1:2. If the

Question

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

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A 36

B  36\sqrt{2}

C 72

D 96

E 144

asishron29181 · Answer

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

KshtriyaNaveen · Answer

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.

100mitra · Answer

Correct Answer C 72

Side ratio : 1: 2
small side = x,
bigger side = 2x
Angle given = 45° 
 Consider 45-45-90 right angle triangle 
Hypothesis = small side = x
 Property of 45-45-90 Right triangle
Ratio of 3 sides = x : x : √2x  
Height of Parallelogram = (x/√2)

Area of Parallelogram = 36√2
height * base = 36√2
(x/√2) * 2x = 36√2
(X^2) * √2 = 36√2
(x^2) = 36
x = 6 ----- 
small side = 6
Bigger side = 2x = 2*6 = 12
Area of Rectangular = l*w = 6* 12 = 72
 Option C = 72

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sebarm95 · Answer

This is very helpful, thank you! Why does the highlighted section above equa x^2*√2? I would have put it as 3x*√2 Please forgive my ignorance, eager to learn!

100mitra · Answer

Hope it solve the purpose

sebarm95 · Answer

THIS IS INCREDIBLY HELPFUL! THANK YOU!!!

I'm only stuck on one step - did you multiply everything by √2 or did you multiply everything by ^2, on this step?

Many thanks!!

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

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In a parallelogram, the ratio of the two adjacent sides is 1:2. If the

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