Question

1. choose the correct answer.

triangle def with de = 6 cm, ef = 3 cm, df = 5 cm

a = 3 cm, b = 5 cm, c = 6 cm
the triangle is a(n) ____ triangle.

• acute
• obtuse
• right

Explanation:

Step1: Recall triangle type rules

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), we use the Pythagorean theorem and its extensions. The rules are:

• If \(c^{2}=a^{2}+b^{2}\), it's a right triangle.
• If \(c^{2}
• If \(c^{2}>a^{2}+b^{2}\), it's an obtuse triangle.

Step2: Identify the longest side

Here, \(a = 3\space\text{cm}\), \(b = 5\space\text{cm}\), \(c = 6\space\text{cm}\). The longest side is \(c = 6\space\text{cm}\).

Step3: Calculate \(c^{2}\), \(a^{2}+b^{2}\)

Calculate \(c^{2}\): \(c^{2}=6^{2}=36\)
Calculate \(a^{2}+b^{2}\): \(a^{2}=3^{2} = 9\), \(b^{2}=5^{2}=25\), so \(a^{2}+b^{2}=9 + 25=34\)

Step4: Compare \(c^{2}\) and \(a^{2}+b^{2}\)

Since \(36>34\) (i.e., \(c^{2}>a^{2}+b^{2}\)), the triangle is obtuse.

Answer:

obtuse