Question

1. if ( ab = 14 ) and ( ac = 27 ), find the length of ( bc ).

1. if ( ab = 14 ) and ( ac = 30 ), find the length of ( bc ).

Explanation:

Step1: Analyze the relationship between line segments

From the figure, we know that \(AC = AB+BC\). So, we can rewrite the formula to find \(BC\) as \(BC=AC - AB\).

Step2: Substitute the values for \(AB\) and \(AC\) in question 23

Given \(AB = 14\) and \(AC = 27\) in question 23. Substitute these values into the formula \(BC=AC - AB\). So, \(BC=27 - 14\).

$$BC=27 - 14=13$$

Step3: Substitute the values for \(AB\) and \(AC\) in question 24

Given \(AB = 14\) and \(AC = 30\) in question 24. Substitute these values into the formula \(BC=AC - AB\). So, \(BC=30 - 14\).

$$BC=30 - 14 = 16$$

Answer:

1. C. 13
2. A. 16