Question

what is ad? ad =

Explanation:

Step1: Set up an equation

Since $AB = BC = 69$ and the perpendicular - bisector theorem states that if a point is on the perpendicular bisector of a segment, it is equidistant from the endpoints of the segment. So, $4u - 28=7u - 85$.

Step2: Solve for $u$

Subtract $4u$ from both sides: $-28 = 7u-4u - 85$.
Simplify to get $-28 = 3u - 85$.
Add 85 to both sides: $3u=-28 + 85$.
So, $3u = 57$.
Divide both sides by 3: $u=\frac{57}{3}=19$.

Step3: Find the length of $AD$

Substitute $u = 19$ into the expression for $AD$ which is $4u-28$.
$AD=4\times19 - 28$.
$AD = 76-28$.
$AD = 48$.

Answer:

48