Question

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.

Answer 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