The area of a parallelogram is 96 cm squared the height is 4 cm less than the length what is

the length

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!

Area of paralellogram=legnth times height

l=legnth

h=height

area=96

lh=96

h is 4 less than l

h=-4+l

sub

l (-4+l) = 96

-4l+l^2=96

minus 96 both sides

l^2-4l-96=0

factor

(l-12) (x+8) = 0

set to zero

l-12=0

l=12

l+8=0

l=-8, imossible, legnth cannot be negative, disreagard this soultion

legnth=12cm