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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]1). -62). 123). 64). -12 |
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Answer» 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 |
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