The given figure shows a right triangle PQR, which is right-angled at P such that Q=2 PRO. If the perimeter of A PQR is [7√3 (√3+1)] cm , then what is its area?
(A) 27(√3–1)cm²
(B) 27/2 (√3–1)cm²
(C) 49√3cm²
(D) 49/2√3cm²
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Answer:
Given that:
QP=8cm,PR=6cm and SR=3cm
(I) In △PQR and △SPR
∠PRQ=∠SRP (Common angle)
∠QPR=∠PSR (Given that)
∠PQR=∠PSR (Properties of triangle )
∴△PQR∼△SPR (By AAA)
(II)
SP
PQ
=
PR
QR
=
SR
PR
(Properties of similar triangles)
⇒
SP
8cm
=
3cm
6cm
⇒SP=4cm and
⇒
6cm
QR
=
3cm
6cm
⇒QR=12cm
(III)
ar(△SPR)
ar(△PQR)
=
SP
2
PQ
2
=
4
2
8
2
=4
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