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Which rectangle has area 24 cm |
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Answer» th of the rectangle = 12 cms Breadth of the rectangle = 2 cms. Step-by-step explanation: LENGTH of rectangle = x cmLength of the rectangle = 12 cms Breadth of the rectangle =2cms Length of rectangle = x cm Let the breadth of the rectangle be y cm. Area of rectangle = 24cm Therefore, Area of rectangle = l x b 24 cm = XY --------- equ. 1 Now, perimeter of rectangle = 20 cm =2 (l+b) 20 cm= 2 (x+y) 2x + 2y = 20 --------equ. 2 From equ. 2: 2y = 20 - 2x \frac{20 - 2x}{2} = y From equ. 1: \frac{24}{x} = y \: From above equations: \frac{20 - 2x}{2} = \frac{24}{x} 20x - {2x}^{2} = 48 - 2x^{2} + 20x - 48 = 0 2 {x}^{2} - 20x + 48 = 0 2 {x}^{2} - 24X + 4x - 48 = 0 2x(x - 12) + 4(x - 12) = 0 (2x + 4)(x - 12) = 0 2x + 4 = 0 \: and \: x - 12 = 0 2x + 4 = 0 x = - 2 And, x - 12 = 0 x = 12 Now, since. measurement cannot be negative. Therefore, x = 12 Substitute x = 12 in equ. 1: Therefore, xy = 24 12y = 24 y = 2 Therefore, the length of the rectangle is 12 cms and the breadth of the rectangle is 2 cms. Let the breadth of the rectangle be y cm. Area of rectangle = 24cm Therefore, Area of rectangle = l x b 24 cm = xy --------- equ. 1 Now, perimeter of rectangle = 20 cm =2 (l+b) 20 cm= 2 (x+y) 2x + 2y = 20 --------equ. 2 From equ. 2: 2y = 20 - 2x \frac{20 - 2x}{2} = y From equ. 1: \frac{24}{x} = y \: From above equations: \frac{20 - 2x}{2} = \frac{24}{x} 20x - {2x}^{2} = 48 - 2x^{2} + 20x - 48 = 0 2 {x}^{2} - 20x + 48 = 0 2 {x}^{2} - 24x + 4x - 48 = 0 2x(x - 12) + 4(x - 12) = 0 (2x + 4)(x - 12) = 0 2x + 4 = 0 \: and \: x - 12 = 0 2x + 4 = 0 x = - 2 And, x - 12 = 0 x = 12 Now, since. measurement cannot be negative. Therefore, x = 12 Substitute x = 12 in equ. 1: Therefore, xy = 24 12y = 24 y = 2 Therefore, the length of the rectangle is 12 cms and the breadth of the rectangle is 2 cms. |
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