PQR is a right-angled triangle with the right angle at Q and k being the length of the perpendicular from Q on PR. If l, m and n are the lengths of sides PQ, QR, and PR respectively, then which of the following holds true?
1
k
2
=
1
l
2
−
1
m
2
1
k
2
=
1
l
2
+
1
m
2
1
k
2
=
1
m
2
−
1
l
2
1
m
2
=
1
l
2
−
2
k
2
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7th
Maths
The Triangle and Its Properties
Recalling Basics of Triangles and Its Types
PQR is a right - angled tri...
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Asked on December 27, 2019 by
Rittika Bandi
PQR is a right-angled triangle with QS as the perpendicular to the hypotenuse. The ratio PS : SR is equal to
MEDIUM
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ANSWER
In triangles PQS and PQR
∠P is common to both.
and ∠PSQ=∠PQR
Triangles PQS and PQR are equiangular
∴
PQ
PS
=
QR
QS
or, PS=
QR
PQ⋅QS
...(i)
Again, triangles QRS and PQR are equiangular
∴
QR
SR
=
PQ
QS
or, SR=
PQ
QS⋅QR
...(ii)
From eqns. (i) and (ii)
SR
PS
=
QR
PQ⋅QS
⋅
QR⋅QS
PQ
=
QR
2
PQ
2
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