GIVEN :-

• The length of a rectangle EXCEEDS it's breadth by 7cm.
• If the length is decreased by 4 cm and the breadth is increased by 3 cm , the area of NEW rectangle is same as the area of original rectangle.

TO FIND :-

• Length and breadth of original rectangle.

TO KNOW :-

♠ Area of rectangle = l × b

SOLUTION :-

Let the breadth of the rectangle be 'x'cm.

Length exceeds by 7cm , so , length will be 'x+7'cm.

♦ Area of Original Rectangle = x(x + 7)

Now , when the length is decreased by 4cm and breadth is increased by 3cm.

• New length → x + 7 - 4 = 'x+3'cm
• New breadth → 'x+3'cm

♦ Area of New Rectangle = (x+3)(x+3)

Area of Original rectangle is equal to Area of New rectangle.

→ x(x+7) = (x+3)(x+3)

→ x² + 7x = x² + 3x + 3x + 9

→ x² + 7x = x² + 6x + 9

→ x² - x² + 7x - 6x = 9

→ x = 9

★ For Original rectangle,

• Length = x+7 = 9+7 = 16CM
• Breadth = x = 9cm

Hence , length is 16cm and breadth is 9cm for Original rectangle.

MORE TO KNOW :-

♠ Area of SQUARE = side²

♠ Area of triangle = (1/2) × b × h

♠ Area of trapezium = [(sum of parallel sides)/2] × h

♠ Area of semi-circle = πr²/2

♠ Area of parallelogram = l × h

♠ Area of circle = πr²