Question

ABCD is a rectangle are the midpoints of the sides ab BC CD and respectively if KN = 3 cm ab = 5 cm then find BD and LM what kind of quadrilateral is k l m n justify your answer​

Answer 1

kn=3cm

ab=5cm

5*3=15cm

Answer 2

Given :  ABCD is rectangle .

K L M N are the mid points of AB  , BC , CD & DA respectively

KN = 3

To Find :  BD and LM

what kind of quadrilateral is k l m n justify your answer​

Solution:

in ΔABD

K & N are mid points of  AB  & AD

line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to third side

=> KN = BD/2

=> 3 = BD/2

=> BD =  6 cm

also KN || BD

similarly LM = = BD/2  = 3 cm

LM = 3 cm

LM || BD

Hence KN || BD

KN² = AK² + AN²  = (AB/2)² + (AD/2)² = (AB² + AD² )/4

KL² = BK² + BL²  = (AB/2)² + (BC/2)² = (AB² + BC² )/4

BC = AD

hence KN²  = KL²

=> KN = KL

KN = KL = LM = MN

Hence KLMN  is a rhombus

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