S O L U T I O N :
According to the question,
- WY = (6x - 7) units
- XZ = (3x + 2) units
As we know that,
❖ Diagonals of a rectangle are equal.
[tex] \\ \twoheadrightarrow \sf { WY = XZ} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { 6x - 7 = 3x +2} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { 6x - 3x = 2 + 7} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { 3x = 9} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf {x =\dfrac{9}{3} } \\ [/tex]
[tex] \\ \twoheadrightarrow \bf\underline { x = 3} \\ [/tex]
Therefore,
[tex] \\ \twoheadrightarrow \sf { WY \; \& \; XZ = (3x - 2) \; units} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { WY \; \& \; XZ = 3(3) + 2 \; units} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { WY \; \& \; XZ = 9 + 2 \; units} \\ [/tex]
[tex] \\ \twoheadrightarrow \bf\underline { WY \; \& \; XZ = 11\; units} \\ [/tex]
Therefore, length of each diagonal is 11 units.
