Question

The sides of a rectangular field are 80 m and 18 m respectively. The length of the diagonal is :
A) 84 m
B) 98 m
C) 82 m
D) 86 m

Answer 1

Hint: Rectangular field is in a rectangle shape. A rectangle has length and breadth. Every angle in a rectangle is a right angle which means the diagonal will be a hypotenuse and length and breadth will be adjacent sides of the hypotenuse. Use Pythagora's theorem to solve for the length of the diagonal.

Complete step-by-step answer:
We are given the length of sides of a rectangular field are 80 m and 18 m; which means the length of the field is 80 m and breadth of the field is 18 m (length>breadth).

Here, AB and DC are parallel and the lengths of the field; AD and BC are parallel and breadths of the field.
As we can see in the figure, every interior angle of a rectangle is a right angle.
By Pythagoras theorem, in a right angled triangle square of hypotenuse is equal to the sum of squares of its adjacent sides.
Diagonal BD divides the rectangle into two right angled triangles.
Therefore, ABD is a right angled triangle, where BD is the hypotenuse and AB, AD are its adjacent sides.
 $
  B{D^2} = A{B^2} + A{D^2} \\
  AB = 80m,AD = 18m \\
  B{D^2} = {80^2} + {18^2} \\
  B{D^2} = 6400 + 324 \\
  B{D^2} = 6724 \\
  BD = \sqrt {6724} \\
  BD = 82m \\
 $
Therefore, the length of the diagonal BD is 82 m.
So, the correct answer is “Option C”.

Note: A rectangle has 4 sides which are 2 pairs of parallel and equal sides. It has 2 diagonals. Each diagonal divides the rectangle into 2 right angled triangles which means 2 diagonals together will divide the rectangle into 4 right angled triangles and also the diagonals bisect each other.