can the lenghths 12 cm, 13 cm, and 18 cm make a right triangle ? justify your answer
To determine whether the given lengths (12 cm, 13 cm, and 18 cm) can form a right triangle, we can apply the Pythagorean theorem. According to the theorem, for a triangle to be a right triangle, the square of the length of the hypotenuse should be equal to the sum of the squares of the other two sides.
In this case, let's label the sides as follows:
- Side a: 12 cm
- Side b: 13 cm
- Side c: 18 cm (hypotenuse)
Now, we can calculate the squares of these lengths:
- a² = 12² = 144
- b² = 13² = 169
- c² = 18² = 324
To check if the given lengths can form a right triangle, we need to compare this equation: a² + b² = c²
Let's substitute the calculated values:
144 + 169 = 313
Since 313 is not equal to c² (324), the given lengths (12 cm, 13 cm, 18 cm) do not satisfy the condition required to form a right triangle.
Thus, the lengths 12 cm, 13 cm, and 18 cm cannot make a right triangle.