Question

If a parallelogram and a rectangle are of equal area, then the perimeter of parallelogram is less than the perimeter of rectangle.

Answer 1

Step-by-step explanation:

Area of ||gm = base × height, And

Area of rect. = length × width,.

Suppose,W of rect. = B of ||gm

And,L of rect. = H of ||gm

So, Area of rectangle = Area of parallelogram

Here, In area, let height of parallelogram be h,

Breadth be a ,And

length be b.

So, sin(α)=ha

Then h=a sin(α) so Area of the parallelogram = (ab)sin(α)

It will form alpha in parallelogram.

Here, alpha in ||gm is less than 90∘, so sin(α) <1.

Now, we will multiply both sides of that inequality(in text. and ||gm) by ab, and we will get:

(ab)sin(α) < ab

…which means: Area of parallelogram < Area of rectangle.

Note please: sin(a),sin(ab),............ = sina, sinab ............