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

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
An expression for the base of the triangle:. Response area

Equation for the area of the triangle: Response area

The first step in solving for h:

Answer 2

Let's assume the height of the triangle is h cm.
According to the given information, the base of the triangle can be expressed as (3h - 4) cm.

The formula for the area of a triangle is A = (1/2) * base * height.
Using this formula, we have:

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

Multiplying both sides by 2 to eliminate the fraction:

76 = (3h - 4) * h

Expanding the equation:

76 = 3h^2 - 4h

Rearranging the equation to form a quadratic equation:

3h^2 - 4h - 76 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. However, the equation cannot be factorized easily, so let's use the quadratic formula:

h = (-b ± √(b^2 - 4ac)) / 2a

Using the values a = 3, b = -4, and c = -76, we have:

h = (-(-4) ± √((-4)^2 - 4 * 3 * (-76))) / (2 * 3)

Simplifying:

h = (4 ± √(16 + 912)) / 6

h = (4 ± √928) / 6

h ≈ (4 ± 30.463) / 6

Since the height can't be negative, we take the positive value:

h ≈ (4 + 30.463) / 6
h ≈ 34.463 / 6
h ≈ 5.744 cm

Now, let's substitute this value back into the expression for the base:

base = 3h - 4
base = 3(5.744) - 4
base = 17.232 - 4
base ≈ 13.232 cm

Therefore, the height of the triangle is approximately 5.744 cm and the base is approximately 13.232 cm.

Answer 3

An expression for the base of the triangle:

Let's assume the height of the triangle is h cm. According to the given information, the base of the triangle can be expressed as (3h - 4) cm.

Equation for the area of the triangle:

The formula for the area of a triangle is A = (1/2) * base * height. Using this formula, we have:

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

The first step in solving for h:

To find the value of h, we can rearrange the equation for the area of the triangle:

2A = (3h - 4) * h

Expanding:

2A = 3h^2 - 4h

Rearranging:

3h^2 - 4h - 2A = 0

Now we have a quadratic equation in terms of h.