Question

1. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal
areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.​

Answer 1

ANSWER

Parallelogram ABCD and rectangle ABEF on same base AB have equal areas. ....Given

AB=CD ...opposite side of parallelogram

AB=EF ...opposite side of rectangle

and, ∠F=∠E=90

∘

AD>AF and BC>BE ....(Hypotenuse of right angle is greater than other sides )

Now,

Perimeter of □ABCD=AB+BC+CD+DA

Perimeter of □ABEF=AB+BE+EF+FA

Also, CD=EF and AD>AF,BC>BE

∴ Perimeter of parallelogram ABCD> Perimeter of rectangle ABEF.