Question

If the area of a triangle is 2x^2-2x-4 and it has a height of x-2, write the base of the triangle.base of the triangle:_________________

Answer 1

Answer:

The base of the triangle = 4(x + 1)

Explanations:

The Area of a triangle is given by the formula:

$\text{Area = }\frac{1}{2}\times\text{ base }\times\text{ height}$$\begin{gathered} \text{Area = 2x}^2-2x-4 \\ \text{Height = x -2} \end{gathered}$

Substituting these expressions into the formula for the area of a triangle:

$\begin{gathered} 2x^2-2x-4\text{ = }\frac{1}{2}\times\text{ b }\times(x-2) \\ 2(2x^2-2x-4)\text{ = b (x - 2)} \\ 4x^2-4x-8\text{ = b (x-2)} \\ 4x^2-8x\text{ + 4x - 8 = b (x - 2)} \\ 4x(x\text{ - 2) + }4(x\text{ - 2) = b(x-2)} \\ (4x+4)(x-2)\text{ = b(x-2)} \\ b\text{ = }\frac{(4x+4)(x-2)}{(x-2)} \\ b\text{ = 4x + 4} \end{gathered}$

b = 4 (x + 1)

The base of the triangle = 4(x + 1)