In this question, all lengths are in cm and all areas are in cm² - Junior Cycle Mathematics - Question 10 - 2016

For part (b), the area of the rectangle is given as:

$A = xy$

The perimeter can be expressed as:

$P = 2(x + y)$

Equating area to perimeter, we have:

$xy = 2(x + y)$

Rearranging this equation leads to:

$xy - 2y = 2x$

Factoring out y gives:

$y(x - 2) = 2x$

Now, to solve for y, divide both sides by $(x - 2)$ (ensuring $x > 2$):

y = rac{2x}{x - 2}

Thus, we've found y expressed in terms of x.