Question

1. if δpqr ~ δtsr, find sr.

Explanation:

Step1: Use Similar Triangles Proportion

Since \(\triangle PQR \sim \triangle TSR\), the corresponding sides are proportional. So, \(\frac{PQ}{TS}=\frac{QR}{SR}=\frac{PR}{TR}\). We can use \(\frac{QR}{SR}=\frac{PR}{TR}\), where \(QR = 38\), \(SR = 2x - 1\), \(PR = 60\), \(TR = 4x - 26\). Thus, \(\frac{38}{2x - 1}=\frac{60}{4x - 26}\).

Step2: Cross - Multiply

Cross - multiplying gives \(38(4x - 26)=60(2x - 1)\).

Step3: Expand Both Sides

Expanding: \(38\times4x-38\times26 = 60\times2x-60\times1\), \(152x - 988=120x - 60\).

Step4: Solve for x

Subtract \(120x\) from both sides: \(152x-120x - 988=120x - 120x- 60\), \(32x - 988=- 60\). Add 988 to both sides: \(32x=988 - 60\), \(32x = 928\). Divide both sides by 32: \(x=\frac{928}{32}=29\).

Step5: Find SR

Now, substitute \(x = 29\) into \(SR = 2x - 1\). So, \(SR=2\times29 - 1=58 - 1 = 57\).

Answer:

\(57\)