A quadratic equation when the perimeter and diagonal of a rectangle are given.

If the length and width of the rectangle are a and b, what's the formula for the perimeter?

How about the formula for the diagonal?

Now solve that first equation (the perimeter one) for one of the variables (e.g. a = ?). Then just substitute that value into the second equation (the diagonal one). The result will be a quadratic equation in just one variable.

If you're still unsure what to do, try to at least answer the first two questions I posed, then post back with your results. We'll help you go from there.

Can u please tell me the formula for the diagonal of rectangle.

The diagonal forms a right triangle with two of the sides. So it's length is just the Pythagorean theorem:



Just substitute your value for D (the diagonal) and the solution for a or b from the perimeter equation.