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.
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
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