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Is a triangle of the three sides long triangle consecutive 9 centi 12 centi and 18 centi is a right triangle? Explain! |
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Answer» // a, B and c = the sides of the triangle h = HALF around the triangle c = circumference of triangle A tri = triangular area // // on the right elbow triangle there is phytagoras formula where c² = a² + b² // // proof 1 // c² = a² + b² (18cm) ² = (9cm) ² + (12cm )² 324cm² = 81cm² + 144cm² 324cm² ≠ 225cm² // not the same // // proof 2 // s = c / 2 = (9cm + 12cm + 18cm) / 2 = 39cm / 2 = 19.5cm // on the right elbow triangle a and b are the base and HEIGHT of the triangle // A tri = A tri a × t / 2 = √s (s - a) (s - b) (s - c) 9cm × 12cm / 2 = √19.5cm (19.5cm - 9cm) (19.5cm - 12cm) (19.5cm - 18cm) 9cm × 6CM = √19,5cm (10,5cm) (7.5cm) (1.5cm) 54cm² = √204,75cm² (11,25cm²) 54cm² = √2303,4375cm⁴ 54cm² ≠ 47,99..cm² // not the same // so the triangle is not a right angled triangle |
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