Shark teeth are shape like a triangle. The height of a certain shark is 2cm longer than the base. The area is 24cm^2. Find the height and base
base --- x cm
height -- x+2 cm
(1/2)(x)(x+2) = 24
x^2 + 2x - 48 = 0
(x+8)(x-6) = 0
x = -8 or x=6 , (x = -8 is rejected, can't have a negative base)
base is 6 cm
height is 8 cm
To find the height and base of the shark's teeth, let's start by defining the height and base of the triangle:
Let's assume the length of the base of the triangle-shaped shark tooth is "x" cm.
According to the given information, the height of the shark tooth is 2 cm longer than the base. So, the height can be represented as "x + 2" cm.
We know that the area of a triangle can be calculated using the formula:
Area = (base * height) / 2.
Given that the area is 24 cm², we can substitute the values into the formula:
24 = (x * (x + 2)) / 2.
To solve this equation, we'll start by multiplying both sides of the equation by 2 to remove the denominator:
48 = x * (x + 2).
Now, let's simplify the equation:
48 = x^2 + 2x.
Rearranging the equation into a quadratic form:
x^2 + 2x - 48 = 0.
To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, factoring may be easier:
(x + 8)(x - 6) = 0.
So we have two possible solutions for x: x + 8 = 0 or x - 6 = 0.
If x + 8 = 0, then x = -8. Since length cannot be negative, we can disregard this solution.
If x - 6 = 0, then x = 6.
Therefore, the base of the shark tooth is 6 cm.
To find the height, we'll substitute the value of x into the equation for the height:
height = x + 2 = 6 + 2 = 8 cm.
So, the height of the shark tooth is 8 cm and the base is 6 cm.