Question

Find the perimeters of (i) ΔABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?

Answer 1

1) Perimeter of ΔABE = AB + BE + EA

2) Perimeter of rectangle = 2 (Length + Breadth)

Perimeter (ΔABE) > Perimeter (BCDE)

Answer 2

Given, sides of triangle ABE =`5/2 "cm", 2 3/4 "cm" and 3 3/5 "cm"`

And the length of the rectangle BCDE =`2 3/4 "cm"`

And the width of the rectangle BCDE =`7/6 "cm"`

Thus, perimeter of triangle and rectangle = ?

And whose perimeter is greater?

Calculation of Perimeter of Triangle ABE

We know that the perimeter of a triangle = the sum of the three sides of the triangle

=`5/2 + 2 3/4 + 3 3/5 "cm"`

=`5/4 + 11/4 + 18/5 "cm"`

= `(5 xx 10) + (11 xx 5) + (18 xx 4)/20 "cm"`

= `(50 + 55 + 72)/20 "cm"`

=`177/20"cm"`

=`8 17/20 "cm"`

Thus, perimeter of triangle ABE =`8 17/20 "cm"`

Calculation of Perimeter of Rectangle BCED

We know that Perimeter of rectangle = 2 (Length + Breadth)

Thus, the perimeter of the rectangle BCDE =`2 (2 3/4 + 7/6) "cm"`

=`2(11/4 + 7/6)"cm"`

=`2(((11 xx 3) + (7 xx 2))/12) "cm"`

=`2((33 + 14)/12) "cm"`

=`2 xx 47/(2 xx 6) "cm"`

=`47/6 "cm"`

=`7 5/6 "cm"`

`"Thus, the perimeter of the triangle" = 8 17/20 "cm" "and the perimeter of the rectangle =" 7 5/6 "cm" "And the perimeter of the triangle is greater than the perimeter of the rectangle."`