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Find the lengths of the diagonals of rectangle WXYZ.
WY= 6x - 7
XZ = 3x + 2

Answers

Answer 1

Lengths of diagonals of the rectangle are [tex]\boldsymbol{11}[/tex] units, [tex]\boldsymbol{11}[/tex] units respectively.

To understand the calculations, check below.

Define rectangle.

A rectangle is a parallelogram in which each angle is a right angle.

Diagonals of a rectangle are equal.

   [tex]WY=XZ[/tex]

[tex]6x-7=3x+2[/tex]

     [tex]3x=9[/tex]

      [tex]x=3[/tex]

So,

[tex]WY=6x-7\\WY=18-7\\WY=11\\XZ=3x+2\\XZ=9+2\\XZ=11[/tex]

So, lengths of diagonals are [tex]\boldsymbol{11}[/tex] units, [tex]\boldsymbol{11}[/tex] units respectively.

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Answer 2

The length of the diagonals of rectangle are 11 units.

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Given the length of  diagonals rectangles,

WY =  6x - 7

XZ = 3x + 2

The length of the diagonals of any rectangle are equal,

so WY = XZ

6x - 7 = 3x + 2

6x - 3x = 2 + 7

3x = 9

x = 9/3

x = 3

substitute the values

WY = 6x - 7 = 6(3) - 7

WY = 18 - 7 = 11 units

XZ = 3x + 2

XZ = 3(3) + 2

XZ = 9 + 2 = 11 units

Hence the length of the diagonals of rectangle is 11 units.

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