Question

8. Is ABC a right triangle? Explain. B 5 A 14 C 9.2​

Answer 1

Answer: No, it is not.

Explanation:

To figure out if a shape is a right triangle, we need to use the pythagorean theorem, which states that a^2 + b^2 = c^2.

In this case, a is equal to 5, b is equal to 9.2, and c is equal to 14.

a^2 is equal to 25 and b^2 is equal to 84.64, we can add these two values together to get 109.64.

Now, we calculate 14^2, which is 196.

We now have something to determine, is 109.64 equal to 196?

Since these two numbers are not equal to each other, the answer is no, and that means this triangle is not a right triangle.

Answer 2

Triangle ABC is not a right triangle, as the sum of the squares of the shortest two sides do not equal to the square of the longest side.

Explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:

`\boxed{a^2+b^2=c^2}`

where:

• a and b are the legs of the right triangle.
• c is the hypotenuse (longest side) of the right triangle.

As we have been given the measures of all three sides of triangle ABC (where AB and AC are the shortest sides, and BC is the longest side), we can use Pythagoras Theorem to determine if the triangle is a right triangle.

If triangle ABC is a right triangle, then AB and AC will be the legs, and BC will be the hypotenuse.

Substitute the values into the formula:

`\implies AB^2+AC^2=BC^2`

`\implies 5^2+9.2^2=14^2`

`\implies 25+84.64=196`

`\implies 109.64=196`

As 109.64 does not equal 196, triangle ABC is not a right triangle.