Maths-
General
Easy

Question

A child travels 13 m to cross a rectangular field diagonally. If the length of the field is 5 m, find its area.

The correct answer is: Area of the given rectangular plot is 60 m2


    Hint:-
    Area of a rectangle = length * breadth
    All angles in a rectangle are equal to 90°
    Diagonal of a rectangle divides it into 2 right angled triangles.
    Step-by-step solution:-
    In the adjacent diagram, we can see that the diagonal divides the given rectangle into 2 right angled triangles.
    Also, diagonal of the rectangle becomes the hypotenuse of the 2 triangles.
    Hypotenuse of the given triangles = diagonal of the given rectangle = 13m
    Now, 1 side of the rectangle = 1 side of the triangle = 5m
    Let the other side be x m
    By applying Pythagorean theorem, For a right angled triangle-
    Hypotenuse2 = sum of the squares of the remaining 2 sides
    ∴ (13)2 = x2 + (5)2
    ∴ 169 = x2 + 25
    ∴ 169 - 25 = x2
    ∴ 144 = x2
    ∴ x = 12 .............................. (Taking square root both the sides) ........................ (Equation i)
    Area of the given plot = length * breadth
    ∴ Area of the given plot = 12 * 5 ...................................................................................... (From given information & Equation i)
    ∴ Area of the given plot = 60 m2
    Final Answer:-
    ∴ Area of the given rectangular plot is 60 m2.

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