Given ax + by = 4 where a and b can be any of -1 or 1. Using all possible combinations 4 straight lines are possible which when plotted on graph paper enclose a square with area A sq. units. If rectangle of same area is required with integer lengths such that at least of the length is not perfect power of 2 then find perimeter of the required rectangle.
Answers
Answer:
900
Step-by-step explanation:
it is the question things to be written
300/3=100
300+100+500
Given : ax + by = 4 where a and b can be any of -1 or 1. Using all possible combinations 4 straight lines are possible which when plotted on graph paper enclose a square with area A sq. units
To find : Area and Equal area rectangle
Solution:
x -x - y = 4 x + y = 4 -x+y = 4 x - y = 4
-4 0 8 0 -8
-3 -1 7 1 -7
-2 -2 6 2 -6
-1 -3 5 3 -5
0 -4 4 4 -4
1 -5 3 5 -3
2 -6 2 6 -2
3 -7 1 7 -1
4 -8 0 8 0
Vertex are (0 , - 4) , ( 4 , 0) , (0 , 4) , (-4 , 0)
Side length = 4√2
Area = 4√2 * 4√2 = 32 sq units
32 = 1 * 32 or 32 = 2 * 16
Perimeter = 2(1 + 32) = 66 unit
Perimeter = 2(2 + 16) = 36 unit
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