A triangle has sides of length 7 cm, 24 cm, and 25 cm. Is it a right triangle? If so, find its area.
["Is Triangle with Sides 7 cm, 24 cm, and 25 cm a Right Triangle? Find Its Area", "When it comes to geometry, recognizing right triangles is fundamental, and one of the easiest ways to confirm this is by applying the Pythagorean theorem. Today, we examine a triangle with side lengths of 7 cm, 24 cm, and 25 cm: Is it a right triangle? And if so, what is its area?", "### Is This Triangle a Right Triangle?", "A triangle is classified as a right triangle if the lengths of its sides satisfy the Pythagorean theorem:\n[ a^2 + b^2 = c^2 ]\nwhere ( c ) is the longest side (hypotenuse), and ( a ) and ( b ) are the other two sides.", "For the given sides:\n- ( a = 7 ) cm\n- ( b = 24 ) cm\n- ( c = 25 ) cm (the largest side)", "Now apply the theorem:\n[ 7^2 + 24^2 = 49 + 576 = 625 ]\n[ 25^2 = 625 ]", "Since ( 7^2 + 24^2 = 25^2 ), the triangle is a right triangle.", "### Calculating the Area of the Right Triangle", "The area ( A ) of a right triangle is calculated using:\n[ A = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height} ]\nHere, the two perpendicular sides (legs) are 7 cm and 24 cm.", "[ A = \frac{1}{2} \ imes 7 \ imes 24 = \frac{1}{2} \ imes 168 = 84 \ ext{ cm}^2 ]", "---", "### Summary", "- This triangle with sides 7 cm, 24 cm, and 25 cm is a right triangle because it satisfies the Pythagorean theorem.\n- The area is 84 cm², derived from its two legs measuring 7 cm and 24 cm.", "This simple validation confirms not only the triangle's classification but also enables practical geometric calculations—essential for students, architects, engineers, and math enthusiasts alike!"]
