Question

use the figure below to answer questions 1 - 2. 1. classify by sides and angles: a) △pqr b) △qrt c) △rst 2. if pq = 3x + 4 and the perimeter of △pqr = 57, find the value of x.

Explanation:

Step1: Identify equal - side markings

From the figure, we can see that in \(\triangle PQR\), assume \(PQ = QR = PR\) (since there are equal - side markings). The perimeter of \(\triangle PQR\) is the sum of its three sides. Let \(PQ=3x + 4\). Since \(PQ = QR=PR\), the perimeter \(P = PQ+QR + PR=3(3x + 4)\).

Step2: Set up the perimeter equation

We know that the perimeter of \(\triangle PQR\) is \(57\). So, \(3(3x + 4)=57\).
First, divide both sides of the equation by \(3\):
\(3x+4=\frac{57}{3}=19\).
Then, subtract \(4\) from both sides:
\(3x=19 - 4=15\).
Finally, divide both sides by \(3\):
\(x = 5\).

Answer:

\(x = 5\)