Answer:
The values of x which would give an area of 240m² would be:
[tex]x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}[/tex]
Step-by-step explanation:
Given
The base of triangle b = 2x+1
The height of triangle h = 6x-3
The Area of the triangle A = 240 m²
The Area of the triangle has the formula
A = 1/2 × b × h
substituting b = 2x+1, h = 6x-3 and A = 240
[tex]240\:=\:\frac{1}{2}\:\left(2x+1\right)\:\times \left(6x-3\right)[/tex]
[tex]480=\left(2x+1\right)\left(6x-3\right)[/tex]
[tex]480=12x^2-3[/tex]
Subtract 480 from both sides
[tex]12x^2-3-480=480-480[/tex]
[tex]12x^2-483=0[/tex]
[tex]3\left(4x^2-161\right)=0[/tex]
[tex]3\left(2x+\sqrt{161}\right)\left(2x-\sqrt{161}\right)=0[/tex]
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
[tex]2x+\sqrt{161}=0\quad \mathrm{or}\quad \:2x-\sqrt{161}=0[/tex]
solving
[tex]2x+\sqrt{161}=0[/tex]
[tex]2x=-\sqrt{161}[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{-\sqrt{161}}{2}[/tex]
[tex]x=-\frac{\sqrt{161}}{2}[/tex]
also solving
[tex]2x-\sqrt{161}=0[/tex]
[tex]2x=\sqrt{161}[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{\sqrt{161}}{2}[/tex]
[tex]x=\frac{\sqrt{161}}{2}[/tex]
Therefore, the values of x which would give an area of 240m² would be:
[tex]x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}[/tex]
