Answer:
We are given that the area of the parallelogram is 1 m², so we know that the product of the base and height must be 1 m², or:
Base x Height = 1 m²
Substituting in the values given:
(2x - 1) x (4x - 7) = 1
Rearranging to make 4x² the subject:
4x² - 9x + 7 = 0
Subtracting 7 from both sides:
4x² - 9x + 3 = 0
Therefore, 4x² - 9x + 3 = 0
Answer:
See below.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a parallelogram}\\\\$A=bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
Substitute the expressions for b and h and the value of A into the formula for area:
[tex]\implies 1=(2x-1)(4x-7)[/tex]
[tex]\implies (2x-1)(4x-7)=1[/tex]
Expand the brackets:
[tex]\implies 8x^2-14x-4x+7=1[/tex]
[tex]\implies 8x^2-18x+7=1[/tex]
Subtract 1 from both sides of the equation:
[tex]\implies 8x^2-18x+7-1=1-1[/tex]
[tex]\implies 8x^2-18x+6=0[/tex]
Factor out 2 from the left side:
[tex]\implies 2(4x^2-9x+3)=0[/tex]
Divide both sides by 2:
[tex]\implies 4x^2-9x+3=0[/tex]
Hence, showing that 4x² - 9x + 3 = 0.
