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3 years ago

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

Mathematics

1 answer:

Nataly [62]3 years ago

5 0

Answer:

A. 5 < AC < 10

Step-by-step explanation:

If ∆ABC is a right angled triangle, we use the Pythagoras formula:

c² = a² + b²

Where c = longest side

When given sides AB, AC and BC, the formula becomes:

AB² = AC² + BC²

Where AB = Longest side

In the question,

AB = 10 and BC = 5.

10² = AC² + 5²

AC² = 10² - 5²

AC² = 100 - 25

AC² = 75

AC = √75

AC = 8.6602540378

Therefore, the expression that is always true = A. 5 < AC < 10

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