Question

if ac = 35, find the value of each of the following
x
ab
ac
a b c
x + 3 2x + 2

Explanation:

Step1: Set up equation using segment - addition postulate

Since $AC = AB+BC$, and $AB=x + 3$, $BC = 2x+2$, $AC = 35$, we have the equation $(x + 3)+(2x+2)=35$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+2x+3 + 2=35$, which simplifies to $3x+5 = 35$.

Step3: Solve for $x$

Subtract 5 from both sides: $3x=35 - 5=30$. Then divide both sides by 3, so $x=\frac{30}{3}=10$.

Step4: Find the length of $AB$

Substitute $x = 10$ into the expression for $AB$. $AB=x + 3=10+3 = 13$.

Step5: Given value of $AC$

$AC$ is already given as 35.

Answer:

$x = 10$
$AB=13$
$AC = 35$