Question

The base of a triangle is four less then three times the height the area of the triangle is 38 square centimeters

Answer 1

Let's call the height of the triangle h and the base of the triangle b.

According to the problem, the base of the triangle is 4 less than three times the height, so we can write an equation for this:

b = 3h - 4

The area of a triangle is calculated as (1/2) * base * height, so we can use this formula with the given area of 38 square centimeters:

(1/2) * b * h = 38

Substituting the value of b from the first equation into the second equation:

(1/2) * (3h - 4) * h = 38

Expanding the equation, we get:

(3h^2 - 4h) / 2 = 38

Multiplying both sides of the equation by 2:

3h^2 - 4h = 76

Rearranging the equation to make it quadratic:

3h^2 - 4h - 76 = 0

Now we can solve this quadratic equation to find the value of h. We can either factor it or use the quadratic formula:

Using factoring:

(3h + 14)(h - 4) = 0

Setting each factor equal to zero:

3h + 14 = 0 or h - 4 = 0

Simplifying each equation:

3h = -14 or h = 4

Solving for h in each equation:

h = -14/3 or h = 4

Since the height of a triangle cannot be negative, we can disregard the solution h = -14/3.

Therefore, the height of the triangle is 4 centimeters.

Substituting this value into the equation for b:

b = 3h - 4
b = 3(4) - 4
b = 12 - 4
b = 8

So, the base of the triangle is 8 centimeters.

In conclusion, the height of the triangle is 4 cm and the base of the triangle is 8 cm.