Question

triangle abc is shown below. what is the length of line segment ac? 7 9 14 18

Explanation:

Step1: Assume equal - angle sides are equal

Since $\angle B=\angle C$ (not given explicitly but we can assume an isosceles - triangle property based on the problem setup), we have $AB = AC$. So, $2x=3x - 7$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $0=3x - 7-2x$. Simplify to get $x = 7$.

Step3: Find the length of $AC$

Substitute $x = 7$ into the expression for $AC$ which is $3x - 7$. So, $AC=3\times7 - 7=21 - 7=14$.

Answer:

$14$