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In the Following Figure, Ray Pt is the Bisector of ∠Qpr Find the Value of X and Perimeter of ∠Qpr. - Geometry

Sum

In the following figure, ray PT is the bisector of QPR Find the value of x and perimeter of QPR.

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Solution

In Δ PQR, PT is the bisector of P

`"QT"/"TR" = "PQ"/"PR"`

`4/5 = 3.6/"PR"`

 4PR = 18

PR = `18/4= 9/2 = 4.5`cm

 QR =QT +TR

 QR = 4+5 = 9 cm

 Perimeter of Δ PQR =PQ+QR +PR

 3.6+9+4.5 = 17.1 cm

 Perimeter of Δ PQR = 17.1 cm

Concept: Property of an Angle Bisector of a Triangle
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