Question

The sum of the lengths of two adjacent sides of a rectangle is 16 cm and the length of a diagonal is 14 cm. Show that, when the breadth of the rectangle is taken as x cm, it satisfies the quadratic equation ² - 16x + 30 = 0, and find separately the length and the breadth of the rectangle to the first decimal place. (Use 5.83 for the value of √34.)​

Answer 1

To solve for the length and the breadth of the rectangle, we can use the Pythagorean Theorem. By substituting the given values into the theorem, we get that the equation 2x² - 16x + 30 = 0. Therefore, using the quadratic formula, x = 8 ± √34/2. Since the length of the long side is 8 cm, we can calculate the breadth as b = 8 ± √34/2 - 8 = 5.83 ± √34/2 - 5.83. Therefore, the length and breadth of the rectangle are 8 cm and 5.83 cm respectively.