Instead of walking along two adjacent sides of a rectangular field, a boy took a shortcut along the diagonal of the field and saved a distance equal to 1/2 of the longer side. What is the ratio of the shorter side of the rectangle to the longer side?

Asked by Sthitaprajna Mishra | 24th Jul, 2014, 03:41: PM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
G i v e n space t h a t comma z equals x plus y minus y over 2 equals x plus y over 2.... left parenthesis 1 right parenthesis F r o m space t h e space r i g h t space t r i a n g l e comma space A B C comma space b y space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma z squared equals x squared plus y squared.... left parenthesis 2 right parenthesis S u b s t i t u t i n g space t h e space v a l u e space o f space z space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space i n space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e comma open parentheses x plus y over 2 close parentheses squared equals x squared plus y squared rightwards double arrow x squared plus y squared over 4 plus 2 cross times x cross times y over 2 equals x squared plus y squared rightwards double arrow y squared over 4 plus x cross times y equals y squared rightwards double arrow x y equals y squared minus y squared over 4 rightwards double arrow x y equals fraction numerator 3 y squared over denominator 4 end fraction rightwards double arrow x equals fraction numerator 3 y over denominator 4 end fraction rightwards double arrow x over y equals 3 over 4

Answered by Vimala Ramamurthy | 25th Jul, 2014, 10:53: AM