The length and breadth of a rectangular hall in a model are 0.4 m and 30 cm respectively. What is the distance between the opposite corners of the wall in the model?

The correct answer is: Distance between the opposite corners of the wall in the model is 50 cm.

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:-
As per given information-
length of the rectangular hall = 0.4 m = 40 cm (1m = 100 cm. ∴ 0.4 m = 0.4 × 100 cm = 40 cm) .............. (Equation i)
breadth of the rectangular hall = 30 cm ........................................................................................... (Equation ii)
We need to find the distance between the opposite corners of the wall in the model i.e. diagonal for the given rectangular hall.
Let the adjacent diagram represent the given model.
∴ 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
Now, sides of the rectangle = sides of the triangle (other than hypotenuse) = 40 cm & 30 cm
By applying Pythagorean theorem, For a right angled triangle-
Hypotenuse2 = sum of the squares of the remaining 2 sides
∴ Hypotenuse2 = (40)2 + (30)2
∴ Hypotenuse2 = 1,600 + 900
∴ Hypotenuse2 = 2,500
∴ Hypotenuse = 50 cm .......................................................
Final Answer:-
∴ Distance between the opposite corners of the wall in the model is 50 cm.