Math, asked by aiqbal86592, 1 year ago

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

Answered by amitnrw
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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