A rectangular park has a perimeter of 50 m and an area of 150 m². What are its length and breadth?
Answer and explanation
Correct answer: 10 m and 15 m
Let the length and breadth be x and y. From the perimeter, 2(x+y)=50, so x+y=25; from the area, xy=150. Substituting y=25-x gives \(x(25-x)=150\), or \(x^2-25x+150=0\). Factoring, \((x-10)(x-15)=0\), so the dimensions are 10 m and 15 m. Option B has the correct sum of 25 but its product is 144, not 150, so it does not satisfy the area condition. Exam tip: In rectangle problems, use the perimeter to find the sum of the dimensions and the area to find their product.
Frequently asked questions
What is the correct answer to this question?
10 m and 15 m
Why is this the correct answer?
Let the length and breadth be x and y. From the perimeter, 2(x+y)=50, so x+y=25; from the area, xy=150. Substituting y=25-x gives \(x(25-x)=150\), or \(x^2-25x+150=0\). Factoring, \((x-10)(x-15)=0\), so the dimensions are 10 m and 15 m. Option B has the correct sum of 25 but its product is 144, not 150, so it does not satisfy the area condition. Exam tip: In rectangle problems, use the perimeter to find the sum of the dimensions and the area to find their product.
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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