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. Find the length and breadth of the original rectangle .
Answers
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