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?
2 Answers
Explanation:
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
Explanation:
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)#