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The equations of two sides of a square whose area is 25 square units are 3x-4y=0 and 4x+3y=0. The equations of the other two sides of the square are?

The equations of two sides of a square whose area is 25 square units are 3x-4y=0 and 4x+3y=0. The equations of the other two sides of the square are?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
Since this is a square, the two other sides must be parallel to the first two sides. 

So they are: (3x−4y = a) and (4x+3y = b) 
We just need to find values for a and b. 

3x−4y = 0 and 4x+3y = 0 intersect at point (0,0)
Since square has area 25, side length = 5 
So distance from (0,0) to lines (3x−4y = a) and (4x+3y = b) must = 5 

Distance from (0,0) to line (3x−4y = a) = 5 
|3(0) − 4(0) − a| / √(3²+(−4)²) = 5 
|−a| / 5 = 5 
|−a| = 25 
a = ± 25 

Distance from (0,0) to line (4x+3y = b) = 5 
|4(0) + 3(0) − b| / √(4²+3²) = 5 
|−b| / 5 = 5 
|−b| = 25 
b = ± 25 

The other 2 lines are 3x−4y = ± 25 and 4x+3y = ± 25 



There are 4 possible ways to choose the equations for the two other sides: 
4x+3y = 25 and 3x−4y = 25 
4x+3y = 25 and 3x−4y = −25 
4x+3y = −25 and 3x−4y = 25 
4x+3y = −25 and 3x−4y = −25 
 
Regards
Arun (askIITians forum expert)

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