Question

The base of a triangle is 4 less than three times the height. The area of the triangle is 38 square cm. A=b × h / 2

Answer 1

What is the equation for the triangle?

Answer 2

what is the first step in solving for h?

Answer 3

Let's represent the height of the triangle as h.
According to the given information, the base of the triangle is 4 less than three times the height, so the base can be represented as 3h - 4.

The formula for the area of a triangle is A = (base * height) / 2.
Substituting the given values into the formula, we get:
38 = ((3h - 4) * h) / 2

To solve this equation and find the value of h, we can first simplify it:
38 = (3h^2 - 4h) / 2

Multiply both sides of the equation by 2 to eliminate the denominator:
76 = 3h^2 - 4h

Rearrange the equation to set it equal to zero:
3h^2 - 4h - 76 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:
h = (-(-4) ± √((-4)^2 - 4 * 3 * (-76))) / (2 * 3)
h = (4 ± √(16 + 912)) / 6
h = (4 ± √(928)) / 6
h = (4 ± 8√29) / 6

Simplifying further:
h = (2/3)(2 ± 4√29)

Since the height of a triangle cannot be negative, we can ignore the negative solution and only consider the positive solution:
h = (2/3)(2 + 4√29)

Therefore, the height of the triangle is approximately (2/3)(2 + 4√29) cm.

Answer 4

The equation for the area of a triangle is given by:

A = (base * height) / 2

In this case, if we let the base be represented as b and the height as h, the equation becomes:

A = (b * h) / 2

Given that the base is 4 less than three times the height, we can write the base as:

b = 3h - 4

Substituting this expression for the base into the equation for the area, we get:

A = ((3h - 4) * h) / 2

Simplifying this equation, we have:

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

Answer 5

The first step in solving for h is to isolate the variable on one side of the equation.

Starting with the equation:
38 = ( (3h - 4) * h) / 2

First, multiply both sides of the equation by 2 to eliminate the fraction:
76 = (3h^2 - 4h)

Next, move all terms to one side of the equation by subtracting 76 from both sides:
3h^2 - 4h - 76 = 0

Now the equation is in standard quadratic form, and you can proceed to solve it using factoring, completing the square, or the quadratic formula.