The area of a triangle is 54cm².if the height is 3cm more than the base find the length of the base

Answer 1

The area of a triangle is calculated using the equation:

A = 1/2bh where "b" is the base the the triangle and "h" is the height.

We are told that h = b + 3

So, since the area is 54 cm³, then 54 = (1/2)(b)(b + 3)

54 = (1/2)(b)(b + 3)

108 = (b)(b + 3)

108 = b² + 3b

b² + 3b - 108 = 0

(b + 12)(b - 9) = 0

Set each piece equal to zero giving:

b + 12 = 0 or b = -12 and b - 9 = 0 or b = 9

We can through out the answer b = -12 since the base cannot be a negative length. So the base is 9 cm.

Answer 2

(x+3)*x/2=54

(x^2)/2+3x/2=54

x^2+3x=108

x=9

b=9

h=12