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What is the difference in the value of 4x – 3y where x and y are width and length of the rectangle whose perimeter is 60 cm and area is 216? [Consider Length > Width]
What is the difference in the value of 4x – 3y where x and y are width and length of the rectangle whose perimeter is 60 cm and area is 216? [Consider Length > Width]
1). -6
2). 12
3). 6
4). -12
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Length of rectangle = y cm
Width of rectangle = x cm
Area of rectangle = Length × width
⇒ 216 = y × x
⇒ x = 216/y ----(I)
Perimeter of rectangle = 2(Length + width)
⇒ 60 = 2(y + x)
⇒ 30 = y + x
Substitute the value of Eq. (I) in above Equation,
⇒ 30 = y + 216/y
⇒ 30y = y2 + 216
⇒ y2 – 30y + 216 = 0
⇒ y2 – 18y – 12y + 216 = 0
⇒ y (y – 18) – 12 (y – 18) = 0
⇒ (y – 18) (y – 12) = 0
⇒ y = 18 [? Length is larger than width]
⇒ x = 216/18 = 12
∴ Required value = 4x – 3y = 4(12) – 3(18) = 48 – 54 = -6