in a rectangle diagonals Ac and bd intesect at O,given AO = 5x+11 and Co 4x+19 find x. Also find the length of the diagonal
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Diagonals bisect each other in a rectangle and hence
AO = CO ( in this rectangle)
This means that
5x+11=4x+19
Using transposition
5x-4x=19-11
This means that
x= 8 units ( units because the length of rectangle is not given in cm or m)
Now
Diagonal AC = AO + CO
This means that
Ac= 5x+11+4x+19
AC= 9x+30. Now x = 8 , so 9*8 + 30 = 72+30= 102 units.
Now diagonals AC=BD ( diagonals of rectangle are equal) ,
So both diagonals have length equal to 102 units
AO = CO ( in this rectangle)
This means that
5x+11=4x+19
Using transposition
5x-4x=19-11
This means that
x= 8 units ( units because the length of rectangle is not given in cm or m)
Now
Diagonal AC = AO + CO
This means that
Ac= 5x+11+4x+19
AC= 9x+30. Now x = 8 , so 9*8 + 30 = 72+30= 102 units.
Now diagonals AC=BD ( diagonals of rectangle are equal) ,
So both diagonals have length equal to 102 units
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