PQR is an isosceles triangle, right angled at P.
Bisector of angle Q and R meet PR and PQ at S
and T respectively. If QR (in cm) is a two digit
greatest prime number, then (PQ + PR + PS + PT)
is equal to
(1) 388 cm
(2) 194 cm
(3) 97 cm
(4) 291 cm
Answers
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4
Answer:
194 cm
Step-by-step explanation:
QR² = PQ² + PR²
PQ = PR = x (isosceles triangle)
a two digit greatest prime number, = 97
=> 97² = x² + x²
=> x = 97/√2 = 68.6 cm
PQ = PR = 68.6 cm
∠Q = ∠R = 45° ( isosceles triangle)
=> Bisector of angle Q and R = 22.5°
=> Tan 22.5 = PS/PQ = PT / PR
=> 0.414 = PS/68.6 = PT / 68.6
=> PS = PT = 28.4 cm
PQ + PR + PS + PT = 68.6 + 68.6 + 28.4 + 28.4
= 194 cm
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