see the figure in triangle PQR angle PQR=90,seg QS is perpendicular segPR then find x,y,z
Answers
Given : in triangle PQR angle PQR=90,seg QS is perpendicular segPR
To Find : x,y,z
Solution:
in ΔQSR & ΔPSQ
∠QSR = ∠PSQ = 90°
∠SRQ = ∠SQP ( as ∠SRQ = 90° -∠P , ∠SQP = 90° -∠P)
=> ΔQSR ≈ ΔPSQ ( AA Criteria )
QS/PS = SR/SQ = QR/PQ
=> x/10 = 8/x = y/z
=> x² = 80
=> x = 4√5
=> 4√5/10 = y/z
=> 2/√5 = y/z
Area of Triangle
= (1/2) * y * z = (1/2) * PR * SQ
PR = PS + SR = 10 + 8 = 18
=> yz = 18x
=> yz = 18(4√5)
=> yz = 72√5
yz = 72√5
y/z = 2/√5
=> y² = 144 = 12
Z = 6√5
x = 4√5
y = 12
z = 6√5
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