Question

persevere find the values of x and y if △pqs ≅ △rqs.

x=
y=
need help?

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle PQS\cong\triangle RQS\), corresponding sides are equal. So \(PS = RS\) and \(PQ=RQ\).
From \(PS = RS\), we have \(x = 2y\). From \(PQ = RQ\), we have \(2x=3y + 8\).

Step2: Substitute \(x = 2y\) into \(2x=3y + 8\)

Substitute \(x\) in the second equation: \(2(2y)=3y + 8\).
Simplify the left - hand side: \(4y=3y + 8\).

Step3: Solve for \(y\)

Subtract \(3y\) from both sides of the equation \(4y-3y=3y + 8-3y\).
We get \(y = 4\).

Step4: Solve for \(x\)

Since \(x = 2y\) and \(y = 4\), then \(x=2\times4=8\).

Answer:

\(x = 4\), \(y = 4\)