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Two sides of a square lie on the straight lines:-
\[2x+3y+7=0\]
And
\[2x+3y+11=0\]

 

What is the area of the square?

 Jan 23, 2021
 #1
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We  just need to find  the  distance  between  the  lines   ....this will be the  side  of the  square

 

It's possible to derive this with a little work, but I prefer to  use a  formula to calculate the  distance between parallel lines

 

We  have  the forms

 

Ax + By  + C1  =  0

Ax  + By + C2   =  0

 

The  distance  is  given  by

 

l   C1  -C2  l                       l  7  - 11   l                        4

_______________     =   ______________  =       ________  

sqrt  ( A^2 + B^2)             sqrt ( 2^2 + 3^2)             sqrt (13)

 

Area of the  square =   side^2  =  ( 4/ sqrt (13) )^2  =    16/13    units^2

 

cool cool cool

 Jan 23, 2021

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