Question

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle? The triangle is a right triangle because 52 + 122 = 132. The triangle is a right triangle because 5 + 13 > 12. The triangle is not a right triangle because 52 + 132 > 122. The triangle is not a right triangle because 5 + 12 > 13.

Answer 1

Answer:

The Triangle Is A Right Triangle Because 5^2 + 12^2 = 13^2.

Step-by-step explanation:

5^2 = 25. 12^2 = 144. With the Pythagorean theorem, (a^2 + b^2 = c^2), 5 is a, 12 is b, and 13 is c.

25 + 144 = 169.

13 ^ 2 = 169.

Since a^2 + b^2 = c^2 is true, the triangle is a right triangle.

Answer 2

Given:

Sides of triangle= 5cm, 13cm and 12cm

To find: Whether a triangle is a right angled triangle.

This can be solved by applying Pythagorean theorem:

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

$H^2=P^2+B^2$

where,

H= Hypotenuse

P= Perpendicular

B=Base

Applying given values in the formula:

$H^2=P^2+B^2\\\\13^2=5^2+12^2\\\\169=25+144\\\\169=169$

Since, R.H.S= L.H.S

Thus, we can say that this triangle is a right angled triangle.

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