Question

A parallelogram has base (2x - 1) metres and height (4x - 7)m=
The area of the parallelogram is 1 m?.
(1) Show that 4x² - 9x + 3 = 0.
Answer (a)(i)​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Area of the of the paallelogram is 2x-1 and height is 4x-7 }$

$\underline{\textbf{To show:}}$

$\mathsf{4x^2-9x+3=0}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\mathsf{Area\;of\;parallelogram=Base{\times}Height}$

$\textsf{Area of the parallelogram}$

$\mathsf{=Base{\times}Hiehgt}$

$\mathsf{=(2x-1){\times}(4x-7)}$

$\mathsf{=8x^2-14x-4x+7}$

$\mathsf{=8x^2-18x+7}$

$\mathsf{Area\;of\;the\;parallelogram=1}$

$\implies\mathsf{8x^2-18x+7=1}$

$\implies\mathsf{8x^2-18x+6=0}$

$\implies\boxed{\mathsf{4x^2-9x+3=0}}$

Answer 2

Given : A parallelogram has base (2x - 1) metres and height = (4x - 7)m  

The area of the parallelogram is 1 m²

To Find : Show that 4x² - 9x + 3 = 0.

Solution:

Area of parallelogram = base * height

base = 2x - 1   m

height = 4x - 7  m

Area of parallelogram = (2x - 1)(4x - 7)

= 8x²  - 18x + 7

Area of parallelogram =  1 m ²

Equate  area

8x²  - 18x + 7 = 1

=> 8x²  - 18x  + 6 = 0

=> 4x² - 9x + 3 = 0

QED

Hence proved

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