Exercise 17 Page 508

Let's analyze the given quadrilateral WXYZ to find the length ZX. We are told that the figure is a rectangle.

First, by the Segment Addition Postulate, we can express the length of each diagonal as the sum of lengths of its smaller segments. ZX= ZP+PX and WY=WP+PYAdditionally, because a rectangle is a parallelogram, we know that the diagonals bisect each other. This means that point P divides each diagonal into halves. ZP= PX and WP= PY We can use this fact to rewrite the Segment Addition Postulate equations in terms of the given expressions, ZP= 4x-9 and PY= 2x+5.

Now, recall that the diagonals of a rectangle are congruent. Therefore, their lengths are equal. ZX=WY ⇔ 2(4x-9)=2(2x+5) We can use this equation to solve for x.

Now that we know the value of x, we can find ZX using the equation from the table.

We found that the length of ZX is 38.