How to Unravel the Essential Properties of Rectangles

Practice Questions:

1. Imagine a rectangle with a length of \(15\) units and a breadth of \(7\) units. Calculate its area, perimeter, and diagonal length.
2. A rectangle has a perimeter of \(44\) units. If its length exceeds its breadth by \(10\) units, determine the dimensions of this rectangle.
3. Rectangles have a cousin named the square. Given a square with a side measuring \(9\) units, compute its area, perimeter, and diagonal length.

1. Area: \(15 \times 7 = 105\) square units. Perimeter: \(2(15 + 7) = 44\) units. Diagonal: \(\sqrt{15^2 + 7^2} = \sqrt{274} \approx 16.55\) units.
2. Let the breadth be (x). Thus, the length is \(x + 10\). From the given perimeter, \(2(x + x + 10) = 44\). Solving, we get \(x = 12\). So, the breadth is \(12\) units, and the length is \(22\) units.
3. Area: \(9 \times 9 = 81\) square units. Perimeter: \(4 \times 9 = 36\) units. Diagonal: \(\sqrt{9^2 + 9^2} = 9\sqrt{2} \approx 12.73\) units.

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