A classmate drew an acute triangle with sides 9 in. and 12 in. What is the greatest possible whole number that can be the length of the longest side o

alesterp

alesterp

Answered question

2021-06-03

A classmate drew an acute triangle with sides 9 in. and 12 in. What is the greatest possible whole number that can be the length of the longest side of the triangle in inches? Provide evidence.

Answer & Explanation

Mayme

Mayme

Skilled2021-06-04Added 103 answers

By the Pythagorean Inequality Theorem, a triangle is acute if a2+b2>c2a where c is the longest side. So, we can write
92+122>c2
81+144>c2
225>c2
15>c
This means that the longest side must be less than 15 inches. Hence, the e greatest possible whole number that can be the length of the longest side of the triangle is 14 inches.

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