the area of a parallelogram is height multiplied by base. we know the height is 4cm less than length and we want length. let's put everything we know in terms of equations:
l(h) = 96
h = l-4
l is the length and h is the height. now we just need to solve for l. since we don't care about h, we can substitute h= l-4 into lh = 96:
l(l-4) = 96
now we just have to solve for l:
l^2 - 4l - 96 = 0
(l - 12)(l+8) = 0
by the zero product property, either l-12 = 0 OR l+8 = 0. since l+8 = 0 gives l as a negative number, we know that can't be the solutions. therefore, l-12 = 0 and l = 12.
let me know if you have any questions!!!
