Chapter SH, Problem 8.23EP

To determine

To factor polynomial

Answer to Problem 8.23EP

The perimeter of the rectangle is $10x+4$ .

Explanation of Solution

Given information:

Area of the rectangle

  $6x^2+x-15$

Formula used:

Perimeter of the rectangle, $P=2(l+b)$

where,

l is length

b is width

Calculation:

  $A=6x^2+x-15$

On factoring

  $=6x^2+10x-9x-15$

Take common

  $=2x(3x^{}+5)-3(3x+5)$

Take further common from above

  $A=(3x^{}+5)(2x-3)$

From above

  $l=(3x^{}+5)$

  $b=(2x-3)$

Substituting value of l and b in formula

  $P=2((3x+5)+(2x-3))$

On solving,

  $=2(3x+5+2x-3)$

Further solving,

  $=2(5x+2)$

So,

  $P=10x+4$

Hence, the perimeter of the rectangle is $10x+4$ .