Question

6x - 5
3x + 5
which expression represents the area of the triangle?
○ 9x² + 7.5x - 12.5
○ 18x² + 15x - 25
○ 18x²

Explanation:

Step1: Recall triangle area formula

Area = $\frac{1}{2} \times \text{base} \times \text{height}$

Step2: Substitute given values

Area = $\frac{1}{2} \times (3x+5) \times (6x-5)$

Step3: Expand the binomials

$(3x+5)(6x-5) = 3x(6x) + 3x(-5) + 5(6x) + 5(-5) = 18x^2 -15x +30x -25 = 18x^2 +15x -25$

Step4: Multiply by $\frac{1}{2}$

Area = $\frac{1}{2}(18x^2 +15x -25) = 9x^2 +7.5x -12.5$

Answer:

$9x^2 + 7.5x - 12.5$