Answer:
Height of triangle = 6 cm
Step-by-step explanation:
Let,
Height of triangle = h
Base of triangle = b
Given Data:
Area of triangle = A = [tex]36 cm^{2}[/tex]
According to given condition:
h = b - 6
To find out:
Height of triangle = h = ?
Formula:
Area of triangle = A = (b × h)/2
Solution:
Area of triangle = A = (b × h)/2
36 = (b × h)/2
36 × 2 = b × (b - 6 ) ∴h = b - 6
[tex]72 = b^{2} - 6b[/tex]
[tex]b^{2} - 6b - 72 = 0[/tex]
[tex]b^{2} - 12b + 6b - 72 = 0[/tex]
[tex](b^{2} - 12b) +( 6b - 72) = 0[/tex]
[tex]b(b - 12) + 6( b - 12) = 0[/tex]
[tex](b - 12)( b + 6) = 0[/tex]
b- 12 = 0 or b + 6 = 0
b = 12 or b = -6
As base value is always positive, so
Base of triangle = b = 12 cm
h = b - 6
h = 12 - 6
Height of triangle = 6 cm
