InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If the perimeters of a square and rectangle are equal, then A) Both the areas are equal B) Area of square is more than area of rectangle. C) Area of rectangle is more than area of square. D) Area of square is less than area of rectangle. |
|
Answer» Correct option is (B) Area of square is more than area of rectangle. Let length and breadth of rectangle are \(l\;\&\;b\) respectively and side of square be a. \(\therefore\) \(2(l+b)\) = 4a \((\because\) Both have equal parameters) \(\Rightarrow\) \(l+b\) = 2a \(\Rightarrow\) \((l+b)^2=4a^2\) (By squaring both sides) \(\therefore\) Area of square \(=a^2=\frac{(l+b)^2}4\) _________(1) Area of rectangle \(=lb\) Now \(a^2-lb=\frac{(l+b)^2}4-lb\) \(=\frac{(l+b)^2-4lb}4\) \(=\frac{(l-b)^2}4\geq0\) \(\Rightarrow\) \(a^2\geq lb\) \(\Rightarrow\) Area of square \(\geq\) Area of rectangle. B) Area of square is more than area of rectangle. |
|