The area of a triangle is 24 square inches. the height is 4 inches shorter than the base. find the height and the base of the triangle

Area=1/2 times base times height or a=1/2bh

area=24
height=base-4
1/2bh
h=b-4
subitute b-4 for h
1/2b(b-4)
1/2(b^2-4b)
1/2(b^2-4b)=24
multiply by 2
b^2-4b=48
subtract 48 from both sdies
b^2-4b-48=0
factor because if xy=0 then x or/and y=0

find what 2 numbers multiply to get -48 and add to get -4
the numbers are hard to find but they are -9.2111 and 5.2111

so (b-9.2111)(b+5.2111)=0
therefor
b-9.2111=0
add 9.2111
b=9.2111
b+5.2111=0
subtract 5.2111
b=-5.2111
but since the measure can't be negative, we discard this solution

so base=9.2111
subsitute
h=b-4
h=9.2111-4
h=5.2111

height=5.2111 in
base=9.2111 in