The height of a triangle is 7 feet greater than the base. the area of the triangle is 247 ft.² find the length of the base and the height of the triangle

Base = 19

Height = 26

Step-by-step explanation:

Given :

Height, h = base, b + 7 feets

The area of triangle, A = 247 ft²

The area of a triangle is given by :

A = 1/2 * base * height

247 = 1/2 * b * (b + 7)

247 = 0.5 * b * (b + 7)

247 = 0.5b² + 3.5b

0.5b² + 3.5b - 247 = 0

Solving the quadratic equation ; using the quadratic equation solver, the roots are :

b = -26 or b = 19

Length of base can't be negative :

Hence,

Base, b = 19

Height, h = base + 7 = 19 + 7 = 26

Given:

f(x) is an exponential function.

To find:

The value of f(12), to the nearest hundredth.

Solution:

The general exponential function is

For, x=2.5,

         ...(i)

For, x=6.5,

         ...(ii)

Divide (ii) by (i).

Taking 4th root on both sides, we get

Putting b=1.32855 in (i), we get

Now, the required function is

Putting x=12, we get

Therefore, the value of f(12) is 386.422.