Question

Item 7 Find the lengths of the diagonals of rectangle WXYZ . WY=16x+2 XZ=36x−6 The length of each diagonal is ​ units.

Answer 1

To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem and substitute the given values to find the length of the diagonal.

Step-by-step explanation:

To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem. The diagonals of a rectangle are equal in length, so we only need to find the length of one diagonal.

We have the lengths of two sides of the rectangle, WY and XZ. Let's calculate the length of the diagonal using the formula:

Diagonal = sqrt((WY)^2 + (XZ)^2)

Substituting the given values, we get: Diagonal = sqrt((16x+2)^2 + (36x-6)^2)

Simplifying the expression will give us the length of the diagonal.

Answer 2

Because the diagonals of a rectangle are congruent, you would set the two equations equal to each other and solve for x.

16x + 2 = 36x - 6
8 = 20x
x = 8/20, which would simplify into 2/5, or 0.4

Plug the value of x back into one of the equations.

16(0.4) + 2
6.4 + 2
8.4

Check with the other diagonal to confirm.

36(0.4) - 6
14.4 - 6
8.4

The length of each diagonal is 8.4 units.