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.