Question

a rectangular field is 30 m by 40m .what distance is saved by walking diagonally across the field

Answer 1

Length = 30 m.

Breadth = 40 m.


●Diagonal can be found by dividing the rectangle along the diagonal.


This forms 2 congruent right angle triangles.


●According to Pythagorean theorem:


In a right angle triangle, hypotenuse² = adjacent side² + opposite side².


Here:


●diagonal is the hypotenuse.

●length is the adjacent side.

●breadth is the opposite side.


◎Let the diagonal be denoted by the variable x.


So,


x²=30²+40².

x²=900+1600.

x²=2500.

x=√2500.

x=50.


○ Therefore, the length of the diagonal is 50 m.

When the person walks using the length and breadth of the rectangle he covers 30+40 = 70 m, but when he walks using the diagonal of the rectangle he covers 50 m only.

So, he saves 70-50 = 20 m by walking diagonally across it.


●Hence, the person saves 20 meters by walking diagonally across.

Answer 2

if the person walks along the length and breadth of the rectangle:

he walks 30 + 40 = 70m

the length of the diagonal is x

then x² = 30² + 40² ⇒ x = 50

⇒ if he walks diagonally he walks 50m

if he walks diagonally he saves a distance of 70 - 50 = 20m