Chapter ISG, Problem 9.5.2P

To determine

To find dimensions of rectangle.

Answer to Problem 9.5.2P

Length of rectangle $=32in$

Width of rectangle $=11in$

Explanation of Solution

Given information:

Length of rectangle is $4x$

Width of rectangle is $x+3$

Area of rectangle is $A=352i{n}^2$

Formula used:

  $A=lw$

Where

Length of rectangle is l

Width of rectangle is $w$

Calculation:

Length of rectangle $=4x$

Width of rectangle $=x+3$

Area of rectangle, $A=352i{n}^2$

Using formula

  $A=4x(x+3)$

put value of area

  $352=4x(x+3)$

On solving,

  $352=4x^2+12x$

On solving,

  $4x^2+12x-352=0$

On solving,

  $x^2+3x-88=0$

On solving,

  $x^2+11x-8x-88=0$

On solving,

  $x(x+11)-8(x+11)=0$

On solving,

  $(x+11)(x-8)=0$

On solving,

  $(x+11)=0$

  $(x-8)=0$

On solving,

  $x=-11$

  $x=8$

Lenght cannot be negative

Take $x=8$

Length of rectangle $=32in$

Width of rectangle $=11in$