Question

5. Find the perimeters of (i) A ABE (ii) the rectangle BCDE in this
figure. Whose perimeter is greater?​

Answer 1

Answer:

Solution :

From the figure given above ,

i ) Perimeter of ∆ABE

= AB + BE + EA

= 3 1/3 cm + 2 1/5 cm + 4 2/3 cm

= 10/3 + 11/5 + 14/3

= ( 50 + 33 + 70 )/15

=153/15 --------( 1 )

ii ) Perimeter of BCDE

= BC + CD + DE + EB

= DE + BE + DE + BE

[ Since Opposite sides are equal ]

= 2( DE + BE )

= 2 [ 1 2/3 + 2 1/5 ]

= 2 [ 5/3 + 11/5 ]

= 2[ ( 25 + 33 )/15 ]

= 2 × 58/15

= 116/15 ------------( 2 )

From ( 1 ) and ( 2 ) , we observe that

153/15 > 116/153

difference of the perimeter

=153/15 - 116/15

=153-116/15

=37/15

Therefore ,

Perimeter of ∆ABE > Perimeter of BCDE

Perimeter of ∆ABC (37/15) cm greater than perimeter of BCDE.