A foot path of uniform width runs all around inside of a rectangular field 45 m long and 36 m wide. If the area of the path is 234 m², find the width of the path.
Mensuration
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A foot path of uniform width runs all around inside of a rectangular field 45 m long and 36 m wide. If the area of the path is 234 m2, find the width of the path.

KnowledgeBoat · Accepted Answer

Consider ABCD as a rectangular field having, length = 45 m and breadth = 36 m. Let x meters be the width of foot path. We know that, Area = length × breadth From figure, Area of path = Area of rectangle ABCD - Area of rectangle PQRS Substituting the values we get, Area of path = (AB × BC) - (PQ × QR).........(1) From figure, PQ = AB - x - x = (45 - 2x) m, QR = BC - x - x = (36 - 2x) m. Substituting the values in equation (1) we get, ⇒ 234 = (45 × 36) - (45 - 2x) (36 - 2x) ⇒ 234 = 1620 - [45(36 - 2x) - 2x(36 - 2x)] ⇒ 234 = 1620 - (1620 - 90x - 72x + 4x2) ⇒ 234 = 1620 - 1620 + 90x + 72x - 4x2 ⇒ 234 = 162x - 4x2 ⇒ 4x2 - 162x + 234 = 0 ⇒ 4x2 - 156x - 6x + 234 = 0 ⇒ 4x(x - 39) - 6(x - 39) = 0 ⇒ (4x - 6)(x - 39) = 0 ⇒ 4x - 6 = 0 or x - 39 = 0 ⇒ 4x = 6 or x = 39 ⇒ x = = 1.5 or x = 39 Since, width of path cannot be greater than breadth of field, So, x 39 m. Hence, width of path = 1.5 m.

Mathematics

A foot path of uniform width runs all around inside of a rectangular field 45 m long and 36 m wide. If the area of the path is 234 m², find the width of the path.

Mensuration

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