Answer:
height = 4 cm
Explanation:
the area (A) of a triangle is calculated as
A =
bh ( b is the base and h the height )
b is the base then h = b - 8 ( 8 cm shorter than base )
given A = 24 , then
24 =
b(b - 8) ← multiply both sides by 2 to clear the fraction
48 = b(b - 8) = b² - 8b ( subtract 48 from both sides )
0 = b² - 8b - 48 ← in standard form
0 = (b - 12)(b + 4) ← in factored form
equate each factor to zero and solve for b
b - 12 = 0 ( add 12 to both sides )
b = 12
b + 4 = 0 ( subtract 4 from both sides )
b = - 4
but , b > 0 , then b = 12 cm , so
h = b - 8 = 12 - 8 = 4 cm