Question

Find the smallest perimeter and the dimensions for a rectangle with an area of 2525 in. squared g

Answer 1

Answer:

5 in x 5 in

Step-by-step explanation:

The area of the rectangle is given by:

$A=x*y=25\\y=\frac{25}{x}$

Where x and y are the length and width of the rectangle.

The perimeter is:

$P=2x+2y\\P=2x+2*\frac{25}{x}\\ P=2x+\frac{50}{x}$

The value of x for which the derivate of the perimeter function is zero is the length that yields the smallest perimeter:

$P=2x+\frac{50}{x} \\\\P'=2-\frac{50}{x^2} =0\\2x^2=50\\x=5\ in$

The value of y is:

$y=\frac{25}{5}\\y=5\ in$

Therefore, the dimensions that yield the smallest perimeter are 5 in x 5 in.