Sum of 1 and 2 sides of a triangle 11 cm Sum of 2 and third sides 14 cm Perimeter of a triangle 19

| September 9, 2021 | education

Sum of 1 and 2 sides of a triangle 11 cm Sum of 2 and third sides 14 cm Perimeter of a triangle 19 cm Find the sides of the triangle.

Let’s denote the sides of the triangle: the first through x, the second through y and the third through z.
Since the sum of the first and second sides is 11 cm, we have: x + y = 11 cm.
The condition of the task states that the sum of the second and third sides is 14 cm, that is, y + z = 14 cm.
If the perimeter of the triangle is 19 cm, then x + y + z = 19 cm.
Let’s solve the resulting system of three equations with three unknowns.
The first and third equations determine z. We have: 11 cm + z = 19 cm, whence z = 19 cm – 11 cm = 8 cm.
Similarly, the second and third equations determine x. We have: x + 14 cm = 19 cm, whence x = 19 cm – 14 cm = 5 cm.
Now using the first equation, we can easily calculate y. We have 5 cm + y = 11 cm, whence y = 11 cm – 5 cm = 6 cm.
Let’s check the sign of the existence of a triangle with the found dimensions. To do this, we will use a semi-perimeter, which is equal to (19 cm): 2 = 9.5 cm,. We have: for x = 5 cm <9.5 cm; for x = 6 cm <9.5 cm and for z = 8 cm <9.5 cm.This means that the sides of the triangle are 5 cm, 6 cm and 8 cm.



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