Question

1. line l is the perpendicular bisector of segment ab. solve for the follow ac = inches ad = inches ab = inches dc = inches

Explanation:

Step1: Use property of perpendicular bisector

Since line $l$ is the perpendicular bisector of segment $AB$, $AC = BC$. Given $BC = 13$ in, so $AC=13$ in.

Step2: Use Pythagorean theorem in right - triangle $BCD$

In right - triangle $BCD$, $BC = 13$ in and $BD = 12$ in. Let $DC$ be the other leg. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = BC$, $a = BD$ and $b = DC$. So $DC=\sqrt{BC^{2}-BD^{2}}=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5$ in.

Step3: Use property of perpendicular bisector for $AD$

Since line $l$ is the perpendicular bisector of $AB$, $AD = BD$. Given $BD = 12$ in, so $AD = 12$ in.

Step4: Calculate $AB$

$AB=AD + BD$. Since $AD = BD = 12$ in, $AB=12+12 = 24$ in.

Answer:

$AC = 13$ inches
$AD = 12$ inches
$AB = 24$ inches
$DC = 5$ inches