Question

If area of a rhombus and a square with side a is X and Y respectively, then the correct option is​

Answer 1

Answer:

Correct option is

A

1:1

R.E.F image

In ΔABC

AC

2

=x

2

+x

2

⇒

AC=

2

x

Similarly

BD=

2

x

Areaofsquare

Areaofrhombus

=

x

2

2

AC×BD

=

x

2

x

2

=1

Answer 2

Given :- If area of a rhombus and a square with side a is X and Y respectively, then the correct option is :-

A) X : Y = sin θ : 1

B) X : Y = √3 : 2

C) X : Y = 4 : √3

D) X : Y = 3 : 2

Solution :-

We know that,

• Area of square = (side)²
• Area of rhombus = (side)² * value of sin angles between two sides .

Let us assume angles between two sides of rhombus is θ .

so,

→ Area or rhombus with sides as a and angle between side as θ = X = a² * sin θ

and,

→ Area of square with same sides a = Y = a² .

then,

→ X : Y = a²*sin θ : a²

→ X : Y = sin θ : 1 (Ans.) (Option A)

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