A circle is inscribed in ΔPQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5)cm, PQ = (PR + 2)cm. If the perimeter of ΔPQR is 32 cm, then PR is equal to:
Show answer & explanation
Correct answer: B
Explanation
Given:
PQ = QR + 5
PQ = PR + 2
Perimeter of ΔPQR = 32 cm
By formula:
Perimeter = PQ + QR + PR
Let
PR = x
PQ = x + 2
QR = PQ − 5
= (x + 2) − 5
= x − 3
Perimeter
PQ + QR + PR = 32
(x + 2) + (x − 3) + x = 32
3x − 1 = 32
3x = 33
x = 11
PR = 11 cm