Question

A parallelogram and a rectangle has same length of base and a same perimeter. Prove that area of parallelogram is less than the area of rectangle.

Answer 1

Step-by-step explanation:

parallelogram ABCD and rectangle ABEF are on the same Base AB and have equal areas.

They lie between same parallels AB and FC

so,a perpendicular line has the least distance from Base

so, BC>BE &AD>AF (BE perpendicular DC &AF perpendicylar EF)

BC+AD >BE+AF (1)

also,AB=EF&CD=AB (Opposite sides of the llgm)

AB+CD=AB+EF (2)

add eq. 1and 2

AB+BC+CD+AD>AB+BE+EF+AF

the perimeter of parallelogram ABCD is greater than the perimeter of the rectangle ABEF