Question

the side lengths of triangle abc are listed below. ab = 7 mm ac = 12 mm bc = 6 mm which statement about triangle abc is true? a angle a is a right angle b angle b is a right angle c angle c is a right angle d triangle abc is not a right triangle

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Check each option

• Option A (Check if \(\angle A\) is right - angle):

If \(\angle A\) is a right - angle, then \(BC^{2}=AB^{2}+AC^{2}\).
\(AB = 7\), \(AC = 12\), \(BC = 6\)
\(AB^{2}+AC^{2}=7^{2}+12^{2}=49 + 144=193\)
\(BC^{2}=6^{2}=36\)
Since \(36
eq193\), \(\angle A\) is not a right - angle.

• Option B (Check if \(\angle B\) is right - angle):

If \(\angle B\) is a right - angle, then \(AC^{2}=AB^{2}+BC^{2}\)
\(AB^{2}+BC^{2}=7^{2}+6^{2}=49+36 = 85\)
\(AC^{2}=12^{2}=144\)
Since \(85
eq144\), \(\angle B\) is not a right - angle.

• Option C (Check if \(\angle C\) is right - angle):

If \(\angle C\) is a right - angle, then \(AB^{2}=AC^{2}+BC^{2}\)
\(AC^{2}+BC^{2}=12^{2}+6^{2}=144 + 36=180\)
\(AB^{2}=7^{2}=49\)
Since \(49
eq180\), \(\angle C\) is not a right - angle.

Answer:

D. Triangle ABC is not a right triangle