Question

find the values of x and y given that \\( \triangle mnp \cong \triangle tus \\).

Explanation:

Step1: Use the property of congruent triangles (corresponding sides are equal)

Since \(\triangle MNP\cong\triangle TUS\), then \(NP = US\).
We have \(NP=(2x - y)\)m and \(US = 13\)m. So \(2x-y=13\).
Also, \(MP = TS\). Given \(MP = 24\) and \(TS=(2x - 5)\), then \(2x-5 = 24\).

Step2: Solve the equation \(2x-5 = 24\) for \(x\)

Add \(5\) to both sides of the equation \(2x-5 = 24\).
\(2x=24 + 5\), so \(2x=29\), and \(x=\frac{29}{2}=14.5\).

Step3: Substitute \(x = 14.5\) into \(2x-y=13\) to solve for \(y\)

Substitute \(x = 14.5\) into \(2x-y=13\), we get \(2\times14.5-y=13\).
\(29-y=13\). Subtract \(29\) from both sides: \(-y=13 - 29=-16\). Multiply both sides by \(- 1\) to get \(y = 16\).

Answer:

\(x = 14.5\) and \(y = 16\)