Perimeter = Sum of the sides measures
Perimeter = | AB | + | AT | + | BT |
Perimeter = ( x + 3 ) + ( 4x ) + ( 2x + 2 )
40 = x + 4x + 2x + 3 + 2
Colect like terms
40 = ( 1 + 4 + 2 )x + ( 3 + 2 )
40 = 7x + 5
Subtract both sides - 5
40 - 5 = 7x + 5 - 5
35 = 7x
Switch sides
7x = 35
Divide both sides by 7
7x ÷ 7 = 35 ÷ 7
x = 5
_____________________________
AB = x + 3 = 5 + 3 ======》 AB = 8
AT = 4x = 4 × 5 =========》 AT = 20
BT = 2x + 2 = 2(5) + 2 ===》 BT = 12
According to the law of inequality in a triangle, the sum of any two random sides must be greater than the size of the other side which means :
AB + AT > BT
&
AB + BT > AT
&
AT + BT > AB
If the sides is true in the above inequalities, then those sides are able to form a triangle ;
But if even one of the above inequalities is violated, those sides will not be able to form a triangle.
8 + 20 > 12 ( Check )
8 + 12 > 20 ( Nope this inequlity violated )
Thus the measures of the sides can not represent the measures of the sides of a triangle .
And we're done ...