Answer:
the width of the rectangle is 9 cm and its length is 18 cm.
Explanation:
Let's start by assigning variables to the width and length of the rectangle.
Let x be the width of the rectangle, then its length is x+9.
The diagonal of the rectangle is given as 18cm more than its width, so it can be expressed as:
sqrt((x+18)^2 + (x+9)^2)
We can use the Pythagorean theorem to derive this expression.
Now, according to the problem statement, the diagonal is also the hypotenuse of a right triangle with sides x and x+9. Therefore, we can set up the following equation:
(x+18)^2 + (x+9)^2 = x^2 + (x+9)^2
Expanding and simplifying, we get:
x^2 + 36x + 324 + x^2 + 18x + 81 = x^2 + 2x^2 + 18x + 81
Collecting like terms and simplifying further, we get:
x^2 - 18x - 243 = 0
This is a quadratic equation that we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -18, and c = -243.
Plugging in these values and simplifying, we get:
x = 9 or x = -27
Since the width of the rectangle cannot be negative, we can discard the solution x = -27. Therefore, the width of the rectangle is x = 9 cm.
Using this value, we can find the length of the rectangle as x+9 = 18 cm.
Therefore, the width of the rectangle is 9 cm and its length is 18 cm.