Is a triangle of the three sides long triangle consecutive 9 centi 12 centi and 18 centi is a right triangle? Explain!
Answers
// 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
The property is that a side of a triangle is smaller than the sum of other two-
9+12=21
21>18
9+18=27
27>12
12+18=40
40>9