Lengths of two diagonal of a kite are 80 cm and 36 cm. A parallelogram of base 45 cm is equal in area to that of kite. Find the corresponding altitude of parallelogram.
Answers
Answered by
1
Let ABCD be the rhombus with B and D as obtuse angles and perpendicular from D meets AB at E.
Let diagonals AC and BD meet O.
Both △AOB and ΔDEB are right triangles (as perpendicular of a rhombus bisect each other at right angles and DE is perpendicular on the side AB also angle B is common to both.
Therefore, △AOB∼ΔDEB
⇒
DE
AO
=
EB
OB
=
DB
AB
.....CPST
∴DE(p)=AO×
AB
DB
As △AOB is right angled, AB=
AO
2
+BO
2
=
2
73
Hence, p=(
2
55
)×
2
73
48
=36.164
⇒36cm<p<37cm
Similar questions