The perimeter of a rectangular plot of land is 114 metres and its area is 810 square metres.
(i) Take the length of plot as x metres. Use the perimeter 114 m to write the value of the breadth in terms of x.
(ii) Use the values of length, breadth and area to write an equation in x.
(iii) Solve the equation to find the length and breadth of the plot.

Question

The perimeter of a rectangular plot of land is 114 metres and its area is 810 square metres.
(i) Take the length of plot as x metres. Use the perimeter 114 m to write the value of the breadth in terms of x.
(ii) Use the values of length, breadth and area to write an equation in x.
(iii) Solve the equation to find the length and breadth of the plot.

KnowledgeBoat · Accepted Answer

(i) Given, The length of rectangular plot is x metres Perimeter of the rectangular plot = 114 m By formula, ⇒ Perimeter of rectangle = 2(Length + Breadth) ⇒ 114 = 2(x + breadth) ⇒ = x + breadth ⇒ Breadth = (57 - x) meters. Hence, breadth of rectangle = 57 - x. (ii) Given, Area of rectangle = 810 m2 By formula, Area of rectangle = Length × Breadth ⇒ 810 = x(57 - x) ⇒ 810 = 57x - x2 ⇒ x2 - 57x + 810 = 0 Hence, obtained equation is x2 - 57x + 810 = 0. (iii) Solving, ⇒ x2 - 57x + 810 = 0 ⇒ x2 - 27x - 30x + 810 = 0 ⇒ x(x - 27) - 30(x - 27) = 0 ⇒ (x - 30)(x - 27) = 0 ⇒ (x - 30) = 0 or (x - 27) = 0 [Using zero-product rule] ⇒ x = 30 or x = 27. Case 1: If, x = 30 m then breadth = 57 - x = 57 - 30 = 27 m. Case 2: If, x = 27 m then breadth = 57 - x = 57 - 27 = 30 m. Hence, the dimensions of the rectangular plot are 27 m and 30 m.

Mathematics

Quadratic Equations

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