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