Question

PS bisects ∠ QPR and PS ⊥ QR. If PQ= 2x units, (4)

PR= (3y+8) units, QS= x units and SR= 2y units.

Find the values of x and y.​

Answer 1

Step-by-step explanation:

$T[Basic proportionality theorem : If a line is drawn parallel to one side of a triangle, intersecting other two sides at distinct points, then other two sides are divided in the same ratio.]$

$Now,</p><p></p><p>RT∣∣SP</p><p></p><p>and PR is the transversal</p><p></p><p>Therefore,</p><p></p><p>∠SPR=∠PRT....(2)     [Alternate</p><p></p><p>$

$PS is the bisector of ∠QPR</p><p></p><p>∠QPR=∠SPR</p><p></p><p>From (2) and (3)</p><p></p><p>∠PTR=∠PRT</p><p></p><p>$

$Therefore, PT=PR     [Sides opposite to equal angles of a trinagle are equal]</p><p></p><p>Putting PT=PR in (1)</p><p></p><p>SRQS=PTPQ</p><p></p><p>Hence proved.</p><p></p><p>$