n ΔABC, AB = 10 and BC = 5. Which expression is always true? A. 5 < AC < 10 B. AC = 5 C. 5 < AC < 15 D. AC = 10

A. 5 < AC < 10

Step-by-step explanation:

We are given the ∆ABC

To solve for the sides of ∆ABC , we make use of Pythagoras Theorem

Pythagoras Theorem states that:

AB² = AC² + BC²

Where AB = Longest side, hence its length is always more that AC and BC.

In the above Question, we are given the values of AB and BC

AB = 10

BC = 5

Inputting these values into the Pythagoras Theorem,

10² = AC² + 5²

100 = AC² + 25

AC² = 100 - 25

AC² = 75

AC = √75

AC = 8.6602540378

According to the above calculation, we can see that the expression that is always true = Option A "5 < AC < 10"

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743