Find algebraic expressions which give the perimeters and areas of all rectangles with length 1 centimetre more than the breadth.

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Solution

Let the breadth of the rectangle be x cm.

Therefore, the length of the rectangle is (x + 1) cm.

Area of the rectangle = Length × Breadth

= (x + 1) × x cm²

= (x² + x) cm²

Perimeter of the rectangle = 2 (Length + Breadth)

= 2(x + 1 + x) cm

= 2(2x + 1) cm

= (4x + 2) cm

Thus, the algebraic expressions for the area and perimeter of all the rectangles with length 1 cm more than the breadth are x² + x and 4x + 2 respectively.

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