Question

Find the lengths of the diagonals of rectangle WXYZ.

WY = 62 – 7
XZ = 3x + 2
The length of each diagonal is
units.

Answer 1

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.

`\\ \twoheadrightarrow \sf { WY = XZ} \\`

`\\ \twoheadrightarrow \sf { 6x - 7 = 3x +2} \\`

`\\ \twoheadrightarrow \sf { 6x - 3x = 2 + 7} \\`

`\\ \twoheadrightarrow \sf { 3x = 9} \\`

`\\ \twoheadrightarrow \sf {x =(9)/(3) } \\`

`\\ \twoheadrightarrow \bf\underline { x = 3} \\`

Therefore,

`\\ \twoheadrightarrow \sf { WY \; \& \; XZ = (3x - 2) \; units} \\`

• Since, WY = XZ

`\\ \twoheadrightarrow \sf { WY \; \& \; XZ = 3(3) + 2 \; units} \\`

`\\ \twoheadrightarrow \sf { WY \; \& \; XZ = 9 + 2 \; units} \\`

`\\ \twoheadrightarrow \bf\underline { WY \; \& \; XZ = 11\; units} \\`

Therefore, length of each diagonal is 11 units.