Question

if the area of a triangle is (6x^2 - X - 1) square units, then it's possible dimensions in appropriate units are
a) 2x +1 & 3x + 1
b) 3x +1 & 2x - 1
C) 3x - 1 & 2x - 1
d) 3x - 1 & 2x + 1​

Answer 1

$\textbf{Given:}$

$\text{Area of a triangle is}$

$\mathrm{6x^2-x-1}$

$\textbf{To find:}$

$\text{Dimensions of the given triangle}$

$\textbf{Solution:}$

$\text{Let b and h be the base and height of the given triangle respectively}$

$\text{Then,}$

$\mathrm{\dfrac{1}{2}{\times}b{\times}h=6x^2-x-1}$

$\mathrm{b{\times}h=12x^2-2x-2}$

$\mathrm{b{\times}h=12x^2-6x+4x-2}$

$\mathrm{b{\times}h=6x(2x-1)+2(2x-1)}$

$\mathrm{b{\times}h=(6x+2)(2x-1)}$

$\mathrm{b{\times}h=2(3x+1)(2x-1)}$

$\therefore\text{Dimensions are (3x+1) and (2x-1)}$

$\textbf{Answer:}$

$\textbf{option (b) is correct}$