Maths-
General
Easy

Question

The diagonal of a square is 4 √2 cm. Find the length of another diagonals if the diagonal of another square whose area is double that of the first square.

hintHint:

Area of a square = side2
All angles in a square are equal to 90°
Diagonal of a square divides it into 2 right angled triangles

The correct answer is: ∴ Length of the diagonal of another square is 8 cm


    Step-by-step solution:-
    In the adjacent diagram, we can see that the diagonal divides the given square into 2 right angled triangles.
    Also, diagonal of the square becomes the hypotenuse of the 2 triangles.
    Hypotenuse of the given triangles = diagonal of the given square = 4 √2 cm
    Let the sides of the given square be x cm.
    ∴ side of the triangles (other than hypotenuse) = x cm.
    By applying Pythagorean theorem, For a right angled triangle-
    Hypotenuse2 = sum of the squares of the remaining 2 sides
    ∴  (4 √2)2 = x2 + x2
    ∴  16 × 2 =  2 x 2
    ∴  32 = 2 x 2
     i.e. 2 x 2 = 32
    ∴  x2 = 32 / 2
    ∴  x2 = 16
    ∴  x = 4 .............................. (Taking square root both the sides) ........................ (Equation i)
    Area of the given square = side2
    ∴ Area of the given square = 42 ...................................................................................... (From Equation i)
    ∴ Area of the given square = 16 cm2 ................................................................................... (Equation ii)
    As per given information-
    Area of another square = 2 × Area of original square
    ∴ Area of another square = 2 × 16 ..................................................................................... (From Equation ii)
    ∴ Area of another square = 32
    ∴ Side2 = 32 ........................................................................................... (Area of a square = side2)
    ∴ Side2 = 32
    ∴ Side = 4 √2 ......................................................................................... (Equation iii)
    Apllying Pythagorean theorem, For a right angled triangle-
    Hypotenuse2 = sum of the squares of the remaining 2 sides
    ∴ Hypotenuse2 = (4 √2)2 + (4 √2)2 ...................................................................................... (From Equation iii)
    ∴ Hypotenuse2 = 2 (4 √2)2
    ∴ Hypotenuse2 = 2 (16 × 2)
    ∴ Hypotenuse2 = 2 (32)
    ∴ Hypotenuse2 = 64
    ∴ Hypotenuse = 8 ......................................................................................................... (Taking square root both the sides)
    Final Answer:-
    ∴ Length of the diagonal of another square is 8 cm.

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