i need to know how to solve this
shark's teeth are shaped like triangles . the height of a tooth of a certain shark is 2cm longer than the base . the area is 12cm2 find the height and base.
the area of a triangle=(1/2)(base)(height)
12cm^2=(1/2)(base)(base+2)
12=(1/2)(b)(b+2)
solve for b. Then solve for height by plugging by into the first equation.
To solve this problem, we need to use the formula for the area of a triangle, which is given by:
Area = (base * height) / 2
Let's denote the base of the triangle as 'b' and the height as 'h'. We are given that the height is 2cm longer than the base, so we can write the equation:
h = b + 2
We are also given that the area is 12cm², so we can substitute these values into the area formula:
12 = (b * (b + 2)) / 2
To solve for 'b', we need to simplify and solve the equation. Let's multiply both sides of the equation by 2 to eliminate the fraction:
24 = b * (b + 2)
Expanding the brackets, we get:
24 = b² + 2b
Rearranging the equation to isolate the terms on one side, we have:
b² + 2b - 24 = 0
Now, we have a quadratic equation. We can either factor it or use the quadratic formula to solve for 'b'. Let's use factoring:
(b + 6)(b - 4) = 0
Setting each factor to zero, we have:
b + 6 = 0 or b - 4 = 0
Solving these equations, we find:
b = -6 or b = 4
Since the base length cannot be negative (since it's a physical measurement), we discard the negative solution. Thus, the base of the triangle is 4cm.
To find the height, we can substitute the value of 'b' into the equation 'h = b + 2':
h = 4 + 2
h = 6
Therefore, the height of the triangle is 6cm.
In summary, the base of the triangle is 4cm and the height is 6cm.