A square field has a 2 m wide path around it. The total area including the path is 196 m². What is the side of the field?
Answer and explanation
Correct answer: 10 m
Let the side of the inner square field be x metres. A path 2 m wide runs around all four sides, so the outer square gains 2 m on each side at both ends; its side is therefore x + 4, not x + 2. The total outer area is 196 m², giving (x + 4)² = 196. Since a side length is positive, x + 4 = 14, and hence x = 10 m. The negative square-root possibility is not geometrically meaningful. Thus option B is correct. Option A would make the outer side 12 m and area 144 m², while C and D produce outer areas larger than 196 m². The essential modelling concept is converting the uniform surrounding width into the correct outer dimension.
Frequently asked questions
What is the correct answer to this question?
10 m
Why is this the correct answer?
Let the side of the inner square field be x metres. A path 2 m wide runs around all four sides, so the outer square gains 2 m on each side at both ends; its side is therefore x + 4, not x + 2. The total outer area is 196 m², giving (x + 4)² = 196. Since a side length is positive, x + 4 = 14, and hence x = 10 m. The negative square-root possibility is not geometrically meaningful. Thus option B is correct. Option A would make the outer side 12 m and area 144 m², while C and D produce outer areas larger than 196 m². The essential modelling concept is converting the uniform surrounding width into the correct outer dimension.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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