Question

Use the converse of the Pythagorean theorem to decide if the triangles are right, acute or obtuse. Then classify them

label where a, b, c is

Thank you!!

Answer 1

Acute triangle

Explanation:

Pythagoras theorem states that, The square of the longest side of the triangle is equal to the sum of the other two sides of the triangle.

i.e a² + b² = c² [where c is the longest side of the triangle and a and b are the other two sides]

If a² + b² < c² then the triangle is obtuse.

If a² + b² > c² , then the triangle is acute.

If a² + b² = c² , then the triangle is right angled.

Let's solve

From the given diagram, Longest side (c) is √142 and the other two sides (a and b) are 11 and 5 .

Since, a² + b² > c². Therefore The given triangle is acute.

Answer 2

• Acute triangle

Step-by-step explanation:

Pythagoras theorem states that, The square of the longest side of the triangle is equal to the sum of the other two sides of the triangle.

i.e a² + b² = c² [where c is the longest side of the triangle and a and b are the other two sides]

If a² + b² < c² then the triangle is obtuse.

If a² + b² > c² , then the triangle is acute.

If a² + b² = c² , then the triangle is right angled.

Let's solve,

From the given diagram, Longest side (c) is √142 and the other two sides (a and b) are 11 and 5 .

Using Pythagoras theorem,

»
`\sf a^2 + b^2 = c^3`

»
`\sf 11^2 + 5^2 = \sqrt{{142}^(2) }`

»
`\sf 121 + 25 = 142`

»
`\sf 146 > 142`

Since, a² + b² > c². Therefore The given triangle is acute.