Question

the area of a concrete rectangular pathway is 350m square and its perimeter pathway is 90 m.what is the length of the pathway?

Answer 1

X, y - the lengths of the sides of the pathway

The area of a rectangle is the product of the lengths of its sides. The area is 350 m².
$xy=350$

The perimeter of a rectangle is two times the sum of the lengths of its sides. The perimeter is 90 m.
$2(x+y)=90 \ \ \ \ \ \ |\div 2 \\ x+y=45 \ \ \ \ \ \ \ \ \ \ |-x \\ y=45-x$

Substitute 45-x for y in the first equation:
$x(45-x)=350 \\ 45x-x^2=350 \\ -x^2+45x-350=0 \\ -x^2+10x+35x-350=0 \\ -x(x-10)+35(x-10)=0 \\ (-x+35)(x-10)=0 \\ -x+35=0 \ \lor \ x-10=0 \\ x=35 \ \lor \ x=10$

$y=45-x \\ \hbox{for } x=35: \\ y=45-35=10 \\ \\ \hbox{for } x=10: \\ y=45-10=35$

The dimensions of the pathway are 10 m by 35 m.
The length of the pathway is 35 m.