the length of a rectangle exceeds its with by 3 metre if the width is increased by 4 and the length is decreased by 6 the area is increased by 20 to square metre find the dimension of the rectangle
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Given :-
- The length of a rectangle exceeds its with by 3 metre if the width is increased by 4 and the length is decreased by 6 the area is increased by 20 to square metre.
To find :-
- Dimensions of the rectangle
Solution :-
★ Let the breadth of rectangle be x then its length be (x + 3)
→ Area of rectangle = l × b = x(x + 3)
- Width is increased by 4 and the length is decreased by 6 the area is increased by 20 to square metre.
→ New length = (x + 3) - 6 = (x - 3)
→ New breadth = (x + 4)
→ New area of rectangle = (x - 3)(x + 4)
★ According to the question ★
→ (x - 3)(x + 4) + 20 = x(x + 3)
→ x(x + 4)-3(x + 4) + 20 = x² + 3x
→ x² + 4x - 3x - 12 + 20 = x² + 3x
→ x² + x - 12 + 20 = x² + 3x
→ 8 = 3x - x
→ 2x = 8
→ x = 8/2 = 4
Hence,
- Breadth of rectangle = x = 4 m
- Length of rectangle = (x + 3) = 7 m
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