please tell me how to solve this problem

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

(A)1:3

(B)3:4

(C)2:3

(D)1:2

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- Apr 3rd 2009, 06:46 AMrickymylvArea of square
please tell me how to solve this problem

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

(**A**)1:3

(**B**)3:4

(**C**)2:3

(**D**)1:2 - Apr 3rd 2009, 06:51 AMADARSH
- Apr 3rd 2009, 07:28 AMChop Suey
Given a square with sides of length s, the length of the diagonal of the square is equal to $\displaystyle s\sqrt{2}$

The question asks for the ratio of the area of a square to the area of a square drawn on its diagonal. As in:

$\displaystyle \frac{s^2}{(s\sqrt{2})^2}$ - Apr 3rd 2009, 07:35 AMSoroban
Hello, rickymylv!

Quote:

Please tell me how to solve this problem

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

. . $\displaystyle (A)\;1:3 \qquad (B)\;3:4 \qquad (C)\;2:3 \qquad (D)\;1:2$

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. . $\displaystyle d^2 \:=\:s^2+s^2 \:=\:2s^2 \quad\Rightarrow\quad d \:=\:\sqrt{2}\,s$

The area of the square of side $\displaystyle d$ is: .$\displaystyle \left(\sqrt{2}\,s\right)^2 \;=\;2s^2$

Therefore, the ratio of the two areas is . . .

- Apr 3rd 2009, 09:35 AMlebanonhello
let the side of the square be (a),so the area of the first square is a^2,

then by pythegoras , it's diagonal is a√2,and the area of the second square ia (a√2)^2=2(a^2).

therefore the ratio is:a^2 / 2(a^2)=1/2

D is correct.