Question

(III) If the perimeters of a square and a rectangle are same, then which one of the following is true? (a)The area of the square is always equal to the area of the rectangle. (b) The area of the square is always more than the area of the rectangle. (c) The area of the square is more or equal to the area of the rectangle. (d) The area of the square is less or equal to the area of the rectangle​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given: The perimeters of a square and a rectangle are the same.

To find: We have to determine the true statement.

Solution:

Let the side of a square be x cm.

So, its perimeter will be 4x.

Now let the sides of a rectangle be y and z cm.

So, its perimeter will be 2(z+y)

Given that the perimeters of a square and a rectangle are the same.

$4x = 2(y + z) \\ 2x = (y + z)$

The area of a square is x×x.

The area of a rectangle is yz.

Putting (y+z)/2 in place of x we get-

${ \frac{(y + z)}{4} }^{2}$

So, this value is always greater than yz.

Thus the area of the square is always more than the area of the rectangle.

The correct option is b.