Asked by Momof3A's

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

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Answered by Momof3A's
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:
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.

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