Question

Triangle TAB has a perimeter of 40 cmeters. Could the measures of the sides as shown actually represent the measures of the sides of the triangle? Justify your answer.

Answer 1

EXPLANATION

We can apply the Obtuse Triangle Theorem to check if the the measures of the sides appropiately represents the measures of the triangle:

Perimeter = 40 cm = 4x + 2x + 2 + x + 3

Adding like terms:

40 = 7x + 5

Subtracting 5 to both sides:

40 - 5 = 7x

Adding like terms:

35 = 7x

Dividing both sides by 7:

35/7 = x

Simplifying:

`5=x`

Then, by the obtuse triangle theorem, the following relationship should be fulfilled.