Question

WXYZ is a rectangle. If XV = 2x and WV = 3x - 5, find WY.

Rectangle WXYZ, diagonals intersect at V




WXYZ is a rectangle. If XV = 2x and WV = 3x - 5, find WY.

Rectangle WXYZ, diagonals intersect at V




10

20

2

5

Answer 1

To find WY, we first must use the properties of a rectangle. In a rectangle, the diagonals are equal in length, so we can set up the following equation:

XV^2 + WY^2 = WV^2

(2x)^2 + WY^2 = (3x - 5)^2
4x^2 + WY^2 = 9x^2 - 30x + 25
WY^2 = 5x^2 - 30x + 25

Now, we need to find the value of x. Since the diagonals intersect at V, we can use the fact that the diagonals split each other in half, so XV = VY. This means:

2x = WY

Now we can substitute 2x for WY in the equation we found earlier:

(2x)^2 = 5x^2 - 30x + 25
4x^2 = 5x^2 - 30x + 25
-x^2 + 30x - 25 = 0

Now we can solve for x by factoring or using the quadratic formula. From there, we can find WY which equals 2x.