If the area of a rectangle is 1260 cm2 and its perimeter 146 cm, what is the length of a diagonal?

To find the length of the diagonal of a rectangle, we first need to find the length and width of the rectangle. We know that the area of a rectangle is given by the formula:

Area = length * width

And the perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

From the problem, we know that the area is 1260 cm^2 and the perimeter is 146 cm. We can set up the following system of equations to solve for length and width:

length * width = 1260 2 * (length + width) = 146

Solving this system of equations can be a bit tricky, but one way to do it is to express one variable in terms of the other using the area equation, and then substitute that into the perimeter equation.

Let's express width in terms of length:

width = 1260 / length

Now we can substitute this into the perimeter equation:

2 * (length + 1260 / length) = 146 2length + 2520 / length = 146 2length^2 - 146*length + 2520 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = -146, and c = 2520. We can solve this equation for length using the quadratic formula:

length = [-b ± sqrt(b^2 - 4ac)] / (2a)

Solving this gives two possible solutions for length, but only one of them will make sense in the context of the problem (length must be positive).

Once we have the length, we can substitute it back into the equation width = 1260 / length to find the width.

Finally, we can find the diagonal of the rectangle using the Pythagorean theorem:

Diagonal = sqrt(length^2 + width^2)

This will give us the length of the diagonal of the rectangle.