In the adjoining figure pqr= 90°. Seg qs perpendicular side PR, PS=4, PQ=S. Find x,yand z.
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Answer:
Given: in triangle PQR angle PQR-90,seg
QS is perpendicular segPR
To Find : x.y.z
Solution:
in AQSR & APSQ
ZQSR = ZPSQ = 90°
ZSRQ = ZSQP (as ZSRQ = 90° -ZP, ZSQP = 90° -2P)
=> AQSR APSQ (AA Criteria)
QS/PSSR/SQ = QR/PQ => x/10 = 8/x = yiz
=> 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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