Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal of the field and saved a distance equal to half of the longer side. The ratio of shorter side of the rectangle to the longer side is :

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Solution

Let A and B be the length and breadth respectively.
Diagonal of a rectangle (say C)(By Pythagoras theorem):::: C²=A²+B²--let this be (I)

Given,

C+0.5A=A + B
C=0.5A+B-let this be (II)

Puttin II in I

0.25A²+B²+AB=A²+B²

0.25A²+AB=A²

AB=A2-0.25A²

AB=0.75A²

AB/A²=0.75

B/A=3/4

THERFORE THE RATIO IS 3:4

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The diagonal of a rectangular field is 16m longer than the shorter side .the longer side is 14 more than the shorter side then find the length of the side of a field.

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Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal of the field and saved a distance equal to half of the longer side. The ratio of shorter side of the rectangle to the longer side is :

Let A and B be the length and breadth respectively. Diagonal of a rectangle (say C)(By Pythagoras theorem):::: C2=A2+B2--let this be (I) Given, C+0.5A=A + B C=0.5A+B-let this be (II) Puttin II in I 0.25A2+B2+AB=A2+B2 0.25A2+AB=A2 AB=A2-0.25A2 AB=0.75A2 AB/A2=0.75 B/A=3/4 THERFORE THE RATIO IS 3:4