Question

if \\( \triangle cow \cong \triangle pig \\), and \\( co = 25 \\), \\( cw = 18 \\), \\( ig = 23 \\), and \\( pg = 7x - 17 \\), find \\( x \\) and \\( pg \\)

\\( x = \\)

\\( pg = \\)

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle COW\cong\triangle PIG\), their corresponding sides are equal. So \(CW = IG\) (not used here for \(x\) and \(PG\) calculation) and \(CO\) corresponds to \(PI\), \(OW\) corresponds to \(IG\), \(CW\) corresponds to \(PG\). So \(CW = PG\).

Step2: Set up the equation

Given \(CW = 18\) and \(PG=7x - 17\), we set \(7x-17 = 18\).
Add \(17\) to both sides: \(7x=18 + 17\), so \(7x=35\).
Divide both sides by \(7\): \(x=\frac{35}{7}=5\).

Step3: Calculate \(PG\)

Substitute \(x = 5\) into \(PG=7x - 17\). Then \(PG=7\times5-17=35 - 17 = 18\).

Answer:

\(x = 5\)
\(PG=18\)