Question

Do these three numbers 7, 24, 26 represent a right triangle? If not, what type of triangle would it be?

1) Equilateral triangle
2) Isosceles triangle
3) Scalene triangle
4) Obtuse triangle

Answer 1

The numbers 7, 24, and 26 do not form a right triangle as per the Pythagorean theorem. Instead, since all sides have different lengths, the triangle is scalene, and it is an obtuse triangle because the square of the longest side is greater than the sum of the squares of the other two sides.

Step-by-step explanation:

To determine whether the three numbers 7, 24, 26 represent the sides of a right triangle, one can use the Pythagorean theorem (a2 + b2 = c2), where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.

In this case, if these three numbers form a right triangle, then 72 + 242 should equal 262. Calculating this:

• 72 = 49,
• 242 = 576,
• 262 = 676.

Adding the squares of 7 and 24:

49 + 576 = 625,

which is not equal to 676 (the square of 26). Therefore, these sides do not form a right triangle.

Since all sides are of different lengths, the triangle is scalene. Furthermore, because the largest square (676) is greater than the sum of the squares of the other two sides (625), this indicates that the triangle is also obtuse. Thus, these numbers represent an obtuse scalene triangle.