We can now find the values of AB and BC.
AB:& x ⇒ 4
BC:& 2x-4 ⇒ 2( 4)-4=4
Knowing that both AB and BC are 4, and that the perimeter is 32, we can find the value of CA.
Let's try to draw a triangle using segments with these lengths.
This is not a triangle. Since AC is longer than the sum the other two side lengths, it is not possible to make a triangle using these segments.
AB≅ CA
Here we have that AB ≅ CA.
If two sides are congruent, then they have the same measure.
AB=CA ⇒ CA=x
Knowing that the perimeter is 32, we can write and solve an equation to find the value of x.
We can now find the side lengths of the triangle.
AB:& x ⇒ 9
BC:& 2x-4 ⇒ 2( 9)-4=14
CA:& x ⇒ 9
Let's draw the obtained triangle.
We found that when the perimeter is 32, a possible value for x is 9.
BC≅ CA
Here we have that BC ≅ CA.
If two sides are congruent, then they have the same measure.
BC=CA ⇒ CA=2x-4
Knowing that the perimeter is 32, we can write and solve an equation to find the value of x.
We can now find the side lengths of the triangle.
AB:& x ⇒ 8
BC:& 2x-4 ⇒ 2( 8)-4=12
CA:& 2x-4 ⇒ 2( 8)-4=12
Let's draw the obtained triangle.
We found that when the perimeter is 32, another possible value for x is 8.
b We need to consider the three cases we considered in Part A, but this time with a perimeter of 12.
AB≅ BC
In Part A, we found that if AB≅ BC, then we could find x by solving the equation x=2x-4.
x=2x-4 ⇔ x=4By using the fact that the perimeter is 12, we can find the length of CA.
