Exercise 1 Page 434

We are given the following diagram and asked to find the length of AB. Let's consider the given diagram.

As we can see, 5x-11 represents the length of AB. Therefore, to find AB, we need first to calculate the value of x.

Finding x

From the diagram, we see that AC intersects BD at the midpoint C. Moreover, it is perpendicular to BD. Thereby, AC is a perpendicular bisector of BD. Let's use the Perpendicular Bisector Theorem.

By this theorem, A is equidistant from the endpoints of BD. This means that AB and AD have the same measures. From the diagram, we know that the length of AB is 5x-11 and the length of AD is 3x+5. Let's set these expressions equal. 5x-11= 3x+5 Now, we can solve this equation for x.

Finding AB

Now that we know the value of x, we can evaluate the expression 5x-11 and find the length of AB.

The length of AB is 29.