Answer:
and 
Step-by-step explanation:
the perimeter of a rectangle is given by the following equation:
if a rectangle has a perimeter of 76cm and its length is 5 plus the double of its width we can use a system of equations to find the length 
, and the width 
.
For the perimeter of the rectangle
where is its length, and is its width, 76 is the perimeter of the rectangle in cm.
We know that the lengh of the rectangle is 5 plus the double of its width, writing the equation:
Substituting the equation above in
We got that the rectangle width is w=11cm
Substituting w in the equation
We got that the rectangle length is l=27cm
Verifying the values obtained
with l=27 and w=11
Satisfying the equation
The conic section that the above equation represents is a CIRCLE.
Use completing the square for y and put the equation in standard form:
<span>x</span>²<span>+ y</span>²<span> - 4y + [(-4)/2]</span>²<span> - 1 = 0 + [(-4)/2]</span>²
<span>x</span>²<span> + y</span>²<span> - 4y + (-2)</span>²<span> - 1 = 0 + (-2)</span>²
<span>x</span>²<span> + y</span>²<span> - 4y + 4 - 1 = 4 </span>
<span>x</span>²<span> + (y - 2)</span>²<span> - 1 = 4 </span>
<span>x</span>²<span> + (y - 2)</span>²<span> = 4 + 1
</span>x² + (y -2)² = 5
The radius of the circle is the square root of 5. Its center is found at (0,2)
