Okay, so we know the Perimeter is 48m and the Area is 108m²
the formulas you'll need are P = 2(w+h) and A = w*h (w = width and h = height)
so... 2(w+h) = 48 w*h = 108 w+h = 24 w = 108/h w = 24 - h h = 108/w <span>h </span>= 24 - w
Now we choose one of the variables (I'll pick w) and set the two corresponding equations equal to eachother. w = 24 - h = 108/h then, do some algebra to get h² - 24h + 108 = 0
Recall that in the original question they told us that one of the sides is represented by <span>x. So, lets sub in x for h from now on. (I'll explain why at the end)
so, x</span>² - 24x + 108 = 0
this is a qudratic equation and can be factored into (x - 18)(x - 6) = 0
set each factor equal to zero and solve for x
you get x = 18 and x = 6
the reason we subbed in x was because i knew we would get two answers and it might have been confusing to get two answers for h or w. With x though, you can now choose which value you want to assign to which variable.
to check this answer, you can go back to the top with the equations for perimeter and area and plug these numbers into the equation in any order and it should work.
if that all made sense, you should figure out that the dimensions will be 18m by 6m
