Question

the height of a triangle is 8 cm shorter than its base. if the area of the triangle is 24 cm2, find the height of the triangle.

Answer 1

height = 4 cm

Explanation:

the area (A) of a triangle is calculated as

A =
`(1)/(2)` 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 =
`(1)/(2)` 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