Question

The height of a triangle is 4x more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x =the length of the base.

Write a quadratic equation in factored form. Write entire equation

Answer 1

The length of the base is:

3 units

The resulting quadratic is

x² - 3= 0

Explanation:

Base = x

Height = 4x

Area, A = 1/2* base * Height

A = (1/2) * (x) * (4x)

A = 2x² (1)

But, A = 6 (2)

Since (1) = (2);

2x²= 6

x²= 3

Resulting quadratic:

x² - 3= 0

For the difference between 2 squares:

a² - b² = (a-b)(a+b)

Using that identity, we can factorize our quadratic:

(x-3)(x+3) = 0

So, we have 2 roots:

x = 3 and x = -3

Now, noting that length must take a positive value, we go for the first:

x = 3

CONCLUSION:

The length of the base is:

3 units

The resulting quadratic is

x² - 3= 0