Answer:
The base and height of the triangular tooth of the fish are 6 centimetres and 12 centimetres respectively
Step-by-step explanation:
Given:
The height of the fish tooth = 6 centimetres longer than the base
Area of the tooth = 36 square centimetres
To Find:
The base and height of the fish tooth = ?
Solution:
The area of the triangular tooth = area of the triangle
Then
The area of the triangular tooth = [tex]\frac{1}{2}(base \times height)[/tex]
Let the base be x centimetres, then is height is (x+6) centimetres
On substituting the given values,
[tex]36 = \frac{1}{2}[(x) \times (x +6)][/tex]
[tex]36 = \frac{x^2 +6x}{2}[/tex]
[tex]72 = x^2 + 6x[/tex]
[tex]x^2 +6x -72 = 0[/tex]
Solving using the quadratic formula we get
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x = \frac{-6 \pm \sqrt{(6)^2-4(1)(-72)}}{2(1)}[/tex]
[tex]x = \frac{-6 \pm \sqrt{36 +288}}{2}[/tex]
[tex]x = \frac{-6 \pm \sqrt{324}}{2}[/tex]
[tex]x = \frac{-6 \pm 18}{2}[/tex]
[tex]x= \frac{-6 + 18}{2}[/tex] [tex]x= \frac{-6 - 18}{2}[/tex]
[tex]x= \frac{ 12}{2}[/tex] [tex]x= \frac{-24}{2}[/tex]
x = 6 x = - 12
Neglecting the negative value, we have
base is 6 centimetres
Then height will be (x+6) = (6+6) = 12 centimetres
