Answer:
b = 1.52
Step-by-step explanation:
Length of diagonals of a parallelogram = [tex]\frac{10}{12}(245b - 365)[/tex] and [tex]\frac{2}{3}(3b+6)[/tex]
If the given parallelogram is a rectangle,
Length of the diagonals will be equal in measure,
Therefore, [tex]\frac{10}{12}(245b - 365)=\frac{2}{3}(3b+6)[/tex]
245b - 365 = [tex]\frac{12}{10}\times \frac{2}{3}(3b+6)[/tex]
245b - 365 = [tex]\frac{4}{5}(3b+6)[/tex]
5(245b - 365) = 4(3b + 6)
1225b - 1825 = 12b + 24
1225b - 12b = 24 + 1825
1213b = 1849
b = [tex]\frac{1849}{1213}[/tex]
b = 1.52
The value of b in WXYZ a rectangle is 1.52
For WXYZ to be a rectangle, the diagonal must be equal. Therefore,
10/12(245b−365) = 2/3(3b+6)
2450b / 12 - 3650 / 12 = 2b + 4
2450b / 12 - 2b = 3650 / 12 + 4
204.166666667 b - 2b = 304.166666667 + 4
202.166666667 b = 308.166666667
divide both sides by 202.166666667
b = 308.166666667 / 202.166666667
b = 1.52431986558
b = 1.52
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