Question

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

Answer 1

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

Answer 2

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.

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