Question

the area of a square and that of a square drawn on its diagonal are in the ratio 1:^2,1:2,1:3,1:4​

Answer 1

Answer

1 : 2

$\rule{200}2$

Explanation

Let the sides of square be a

Then, the area of square would be a²

Now, by Pythagoras theorem, we can find the length of diagonal

Diagonal = $\sf \sqrt{a^2 + a^2}$

Diagonal = $\sf \sqrt{2a^2}$

Diagonal = $\sf a\sqrt{2}$

So, the square drawn on its diagonal would have sides = a√2

⇒ area of square drawn on diagonal = (a√2)² = 2a²

So, ratio of area of square and that of a square drawn on its diagonal = a²/ 2a²

= 1/2

= 1 : 2

Answer 2

QUESTION :-

The ratio of the area of a square to that of the square drawn on its diagonal is :

A) 1 : 3

B) 1 : 5

C) 1 : 2✔✔

D) 1 : 6

SOLUTION :-

➠ let the side of square be r.

➠ Area of this square = r²

➠ the diagonal of square = √2 r

➠ .°. Area of square = 2r²

➠ Required ratio = r² : 2r²

➠ Required ratio = 1:2.

Hence, option (c) is the right answer.

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