Chapter 9.5, Problem 51E

To determine

To determine the value of $x$ .

Answer to Problem 51E

Breadth= $7m$

Length= $13m$

Explanation of Solution

Given:

  

Area = $91m^2$ .

Calculation:

According to question,

Area = $91m^2$ .

Formula for area of rectangle $=l\times b$

Breadth= $x+2m$

Length= $2x+3m$

Therefore, area of rectangle $=(x+2)\times (2x+3)$

So,

  $91=(x+2)\times (2x+3)$

On solving brackets,

  $91=2x^2+3x+4x+6$

So,

  $91=2x^2+7x+6$

Taking all the terms on one side,

  $2x^2+7x+6-91=0$

So,

  $2x^2+7x-85=0$

Finding the value of $x$

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

On comparing the equation with $a{x}^2+bx+c$

  $a=2,b=7,c=-85$

Substituting the values,

  $x=\frac{-(7)\pm \sqrt{{(7)}^2-4(2)(-85)}}{2(2)}$

Opening brackets,

  $x=\frac{-7\pm \sqrt{49+680}}{4}$

So,

  $x=\frac{-7\pm \sqrt{729}}{4}$

Solving root,

  $x=\frac{-7\pm 27}{4}$

Therefore,

  $x=\frac{-7+27}{4}$ or $x=\frac{-7-27}{4}$

So,

  $x=\frac{20}{4}$

and

  $x=\frac{-34}{4}$

Length can never be negative,

Therefore, $x=5$

Breadth= $x+2m$

Length= $2x+3m$

Substituting value of $x$

Breadth= $5+2$

Breadth= $7m$

Length= $2(5)+3$ = $10+3$

Length= $13m$