The area of a square and that of a square drawn on its diagonal are in the ratio

(a) 1 : $\sqrt{2}$ (b) 1 : 2 (c) 1 : 3 (d) 1 : 4

Open in App

Solution

Let a be the side of the square. Then
Area of the square = a²
Area of the square drawn on the diagona = ${(a \sqrt{2})}^{2} = 2 a^{2}$
Required ratio = a² : 2a² = 1 : 2
Hence, the correct option is (b).

Suggest Corrections

Similar questions

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

1 : 2

If true then enter

1

and if false then enter

0

Q. A point

P

moves inside a square of area

4

sq.units such that it is nearer to point of intersection of its diagonal than any vertex. Area of region traced by

P

is-

A second square is drawn taking its side length equal to the diagonal of a given square. The ratio of the areas of 1 $^{s t}$ to the 2 $^{n d}$ square is -

$A B C D$ is a square. Equilateral triangles $A C F$ and $A B E$ are drawn on the the diagonal $A C$ and side $A B$ respectively. Find area of $△ A C F$ : area of $△ A B E$ .

Q. The ratio of the areas of two squares, one having its diagonal double than the other, is

(a) 1 : 2
(b) 2 : 3
(c) 3 : 1
(d) 4 : 1

Join BYJU'S Learning Program

The area of a square and that of a square drawn on its diagonal are in the ratio (a) 1 : 2 (b) 1 : 2 (c) 1 : 3 (d) 1 : 4

Let a be the side of the square. Then Area of the square = a2 Area of the square drawn on the diagona = a22=2a2 Required ratio = a2 : 2a2 = 1 : 2 Hence, the correct option is (b).

The area of a square and that of a square drawn on its diagonal are in the ratio

(a) 1 : $\sqrt{2}$ (b) 1 : 2 (c) 1 : 3 (d) 1 : 4

Let a be the side of the square. Then
Area of the square = a²
Area of the square drawn on the diagona = ${(a \sqrt{2})}^{2} = 2 a^{2}$
Required ratio = a² : 2a² = 1 : 2
Hence, the correct option is (b).