Chapter ISG, Problem 8.6.2.3P

To determine

Find the dimensions of the rectangle

Answer to Problem 8.6.2.3P

Breadth is 5 cm.

Length is 45 cm.

Explanation of Solution

Given information:

Perimeter of rectangle= $14x+30$

Area of rectangle=225 square centimetres

Length of rectangle= $6x+15$

Formula used:

Area of rectangle= $length\times breadth$

Perimeter of rectangle= $2(length+breadth)$

Calculation:

Substituting the values,

Perimeter= $14x+30$

So,

  $2(6x+15+breadth)$ = $14x+30$

Dividing equation by 2,

  $6x+15+breadth$ = $7x+15$

Now,

  $breadth$ = $7x+15-(6x+15)$

And, $breadth$ = $7x+15-6x-15$

Hence, $breadth$ = $x$ cm.

Now,

Area =225

  $length\times breadth$ =225

Substituting values,

  $(6x+15)\times x=225$

Multiplying values,

  $6x^2+15x=225$

Dividing equation by 3,

  $2x^2+5x-75=0$

Grouping,

  $2x^2+15x-10x-75=0$

Now,

  $x(2x+15)-5(2x+15)=0$

Takingcommon,

  $(x-5)(2x+15)=0$

For equation to be 0, rejecting $(2x+15)$ because dimensions cannot be in negative.

Now,

  $(x-5)$ =0

Hence, $x=5$

Breadth is 5 cm.

Length is $6x+15$ = $6(5)+15$

Length is 45 cm.