Question

Instead of walking along two adjacent sides of
a rectangular field, a boy took short-cut along
the diagonal and saved a distance equal to half
the longer side. Then the ratio of the shorter to
the longer side is
1) 1:2
2) 2:3 3) 1:4 4) 3:4​

Answer 1

Let the Rectangular Field be represented by : ABCD
Let the Length of the Rectangular Field (AB) be : L
Let the Width of the Rectangular Field (BC) be : W
Goal of the Man : To reach the point C
The Man can reach the point C in two ways. They are :
★  Walk along two adjacent sides AB (Length) and BC (Width)
★  Walk along the Diagonal of the field (AC)
Case - 1 : Man walking along two adjacent sides AB and BC
In this case, The Total Distance covered by the Man to reach Point C will be Sum of Lengths of the Sides AB and BC
✪  Total Distance covered by the Man = L + W
Case - 2 : Man walking along the diagonal of the field (AC)
In this case, The Total Distance covered by the Man to reach Point C will be Length of the Diagonal AC
We know that : Diagonal of a Rectangle is the Hypotenuse of the Right angled Triangle formed by the Diagonal and the Adjacent Sides (legs)
From Pythagorean Theorem, We know that :
★  (Hypotenuse)² = (First Leg)² + (Second Leg)²
 (Length of the Diagonal)² = (Length)² + (Width)²
 (AC)² = (L)² + (W)²

Given : Instead of Walking along two adjacent sides of the rectangular field the man took the shortcut along the diagonal of the field and saved the distance of half of the longer side
It means : if he walks along the Diagonal of the field, He saves a distance of half of the longer side (Length of the rectangular field)
It also means : The Difference between the lengths which he walked in the Two cases which are mentioned above should be equal to half of the Length of the rectangular field.




Hope it helps...
Please mark my answer as the brainliest...