Is it possible for a rectangle with a perimeter of 44cm to have the area of 125cm^2 ? If so, find the dimensions of the rectangle.
Figure out the equation in general form.
It is not possible.
The largest area is when the perimeter of 44 describes a square, namely of 11" per side, which gives an area of 11²=121 < 125.
I assume you are in grade 11, so cannot use calculus to explain. But generally, the rectangle with the largest area for the same perimeter is a square.
If it were possible, then we have the equations:
b*h=A
2(b+h)=P
where b,h represent the dimensions of the rectangle, and A and P represent area and perimeters.
You can then solve for b and h given A and P.
To determine if it is possible for a rectangle with a perimeter of 44 cm to have an area of 125 cm², we need to set up an equation.
Let's assume that the length of the rectangle is "L" units and the width is "W" units.
The perimeter of a rectangle is given by the formula: 2(L + W).
Given that the perimeter is 44 cm, we can write the equation: 2(L + W) = 44.
Now, let's consider the formula for the area of a rectangle: A = L * W.
Given that the area is 125 cm², we can write the equation: L * W = 125.
To find the dimensions of the rectangle, we need to solve this system of equations.