Let's analyze the given quadrilateral to find the length of YW. Keep in mind, we have been told that the figure is a rectangle.
By the definition of a rectangle, we know that WXYZ has four right angles. Because of that, the triangle formed by WXZ is a right triangle.
Recall the following theorem.
Pythagorean Theorem
For a right triangle with legs a and b and hypotenuse c, the following is true: a^2+b^2=c^2.
Using this theorem, we can write the following relation.
XW^2 + WZ^2 = XZ^2
Let's substitute the given expressions for XW, WZ, and XZ into the equation.
3^2 + 4^2 = b^2
Let's solve it for b.
Since the length of a segment cannot be negative, we know that XZ=5. Recall that the diagonals of a rectangle are congruent. Therefore, their lengths are equal.
YW=ZX ⇔ YW= 5
