Question

(a) A parallelogram has base (2x - 1) metres and height (4x-7) metres.

The area of the parallelogram is 1 m².
(i) Show that 4x² - 9x +3=0.
Answer (a)(i)

“please show steps and thank you”

Answer 1

See below.

Explanation:

`\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}}`

Given:

• 
  `b = (2x - 1)\;\sf m`

• 
  `h = (4x - 7)\;\sf m`
• 
  `A=1\;\sf m^2`

Substitute the expressions for b and h and the value of A into the formula for area:

`\implies 1=(2x-1)(4x-7)`

`\implies (2x-1)(4x-7)=1`

Expand the brackets:

`\implies 8x^2-14x-4x+7=1`

`\implies 8x^2-18x+7=1`

Subtract 1 from both sides of the equation:

`\implies 8x^2-18x+7-1=1-1`

`\implies 8x^2-18x+6=0`

Factor out 2 from the left side:

`\implies 2(4x^2-9x+3)=0`

Divide both sides by 2:

`\implies 4x^2-9x+3=0`

Hence, showing that 4x² - 9x + 3 = 0.