Question

if the ratio of the diagonal of two square is 4:1 . find the ratio of area?

Answer 1

∵ diagonal of square = √2 × side length
∴ side length = (diagonal of square/√2)

Now, area of square = side length = [(diagonal/√2)]² = diagonal ²/2
Hence , area of square = diagonal²/2

Given,
Ratio of diagonal of two squares = 4 : 1
Let diagonal of first square = 4x
Then, area of first square = (4x)²/2 = 8x²

and diagonal of 2nd square = x
Area of 2nd square = x²/2

Now, ratio of area of squares = 8x²/x²/2 = 16/1
Hence answer is 16 : 1

Answer 2

Hello Dear.

Here is the answer---


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Let the Diagonals of the two squares be 4x and 1x respectively.


 For the square of the Diagonal 4x,

    Using the Formula,

        Diagonal of the square = √2 × Side of the Square 
                                           4x = √2  × Side
                                     ⇒ Side = 4x/√2

Area of the Square(A₁) = (Side)²
                                     = (4x/√2)²
                                     = 16x²/2
                                     = 8x²

For the Square whose diagonal is 1 x,

  Side = 1x/√2

⇒Area(A₂) = 1x²/2
                  = x²/2

Thus, Ratio between the Area of the square A₁ and A₂ is---

         $\frac{A1}{A2} = \frac{ 8x^{2} }{ x^{2}/2}$
        ⇒   $\frac{A1}{A2} = \frac{16}{1}$

Thus, the ratio between the area of the square will be 16:1.


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Hope it helps.


Have a Marvelous Day.