# A rectangular field has an area of #1,764# #m^2#. The width of the field is #13# #m# more than the length. What is the perimeter of the field?

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Let the length of the rectangle be

#color(blue)("Area of a rectangle"=l*w#

Where,

So,

Use the distributive property

Write it in standard form

Now, this is a quadratic equation. We solve it using the quadratic formula

#color(violet)(l=(-b+-sqrt(b^2-4ac))/(2a)#

Where

Then,

Solving this, we get

As, length cannot be negative

The length of the rectangle is

We need to find the perimeter

#color(blue)("Perimeter of rectangle "=2(l+b)#

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If a rectangle has width

In this case

Plugging this expression for W into the formula for area gives us

It is hard to establish the factors of a big number like

We can discount the negative root as the length of a real field cannot be negative. So

Therefore the perimeter

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