Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

a. the triangle is a right triangle because 52 + 122 = 132.
b. the triangle is a right triangle because 5 + 13 > 12.
c. the triangle is not a right triangle because 52 + 132 > 122.
d. the triangle is not a right triangle because 5 + 12 > 13.

 A. The triangle is a right triangle because

Step-by-step explanation:

According to the converse of Pythagoras Theorem,

If in a triangle , The square of the longest sides is equal to the sum of the squares of the other two sides then the triangle is a right triangle .

The given side lengths of triangle = 5 cm, 13 cm, and 12 cm

The longest side = 13 cm

Square of longest side =   (1)

Sum of the square of other two sides =  (2)

From (1) and (2)

Square of longest side =Sum of the square of other two sides

⇒ The triangle is a right triangle.

Hence , the correct option is A. The triangle is a right triangle because

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