Question

this task comes from the on your own questions 10 and 12 and is used as a substitute for the construction. task 2: a. if ab = 49 and bc = 22, what is the length of ac? b. use the figure to solve for x. find ab and bc. turn and talk: if ac = 62 and bc = 27, what is the length of ab?

Explanation:

Step1: Solve part A

Since $AC = AB+BC$, substituting $AB = 49$ and $BC = 22$, we get $AC=49 + 22$.
$AC=71$

Step2: Solve part B

We know that $AB+BC=AC$. Given $AB = 2x - 2$, $BC=x + 5$ and $AC = 36$. So, $(2x-2)+(x + 5)=36$.
Combining like - terms: $2x-2+x + 5=36$ becomes $3x+3 = 36$.
Subtract 3 from both sides: $3x=36 - 3=33$.
Divide both sides by 3: $x = 11$.
Then $AB=2x-2=2\times11-2=20$ and $BC=x + 5=11 + 5=16$.

Step3: Solve Turn and Talk part

Since $AC=AB + BC$, then $AB=AC - BC$. Substituting $AC = 62$ and $BC = 27$, we get $AB=62-27$.
$AB = 35$

Answer:

A. $AC = 71$
B. $x = 11$, $AB = 20$, $BC = 16$
Turn and Talk: $AB = 35$