Question

The expressions 10/12(245b−365) and 2/3(3b+6) represent the lengths of the diagonals of parallelogram WXYZ. For what value of b is WXYZ a rectangle?
b =

Answer 1

Answer:

b = 1.52

Step-by-step explanation:

Length of diagonals of a parallelogram = $\frac{10}{12}(245b - 365)$ and $\frac{2}{3}(3b+6)$

If the given parallelogram is a rectangle,

Length of the diagonals will be equal in measure,

Therefore, $\frac{10}{12}(245b - 365)=\frac{2}{3}(3b+6)$

245b - 365 = $\frac{12}{10}\times \frac{2}{3}(3b+6)$

245b - 365 = $\frac{4}{5}(3b+6)$

5(245b - 365) = 4(3b + 6)

1225b - 1825 = 12b + 24

1225b - 12b = 24 + 1825

1213b = 1849

b = $\frac{1849}{1213}$

b = 1.52