Question

find the area of the given triangle.

Explanation:

Step1: Recall triangle area formula

The area of a right triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.

Step2: Substitute given expressions

Base = $2x+4$, Height = $5x-2$. Substitute into formula:
$\text{Area} = \frac{1}{2} \times (2x+4) \times (5x-2)$

Step3: Simplify the expression

First factor $2$ from $2x+4$:
$\frac{1}{2} \times 2(x+2) \times (5x-2) = (x+2)(5x-2)$
Expand the product:
$x(5x-2) + 2(5x-2) = 5x^2 - 2x + 10x - 4$
Combine like terms:
$5x^2 + 8x - 4$

Answer:

$5x^2 + 8x - 4$