Question

The length of the given rectangle is x cm and its perimeter is 12 cm.

Show that the area, A, of the rectangle is given by A = 6x - x².
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Answer 1

The given figure is that of a rectangle, having one angle as 90° and diagonals equal.

Given length of rectangle: x cm

• Perimeter = 12 cm

We know perimeter f the r rectangle:

• 2(length + width) = P

Put the values:

• 2(x + width) = 12

Divide both sides by 2:

• x + width = 12/2 = 6

Subtract x from both sides:

• width = 6-x

We know area of rectangle :

• Ar(Rect.) = length*width

Putting the values:

• Ar(Rect.) = x(6-x) = 6x - x² ( Apply Distributive property)

Hence, proved that Ar(Rect.) = 6x - x²