Question

The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.

Answer 1

Let the breadth of rectangle be x cm.

According to the question:

Side of the square =`(x+4)cm` 

Length of the rectangle=`{3(x+4)}` cm  

It is given that the areas of the rectangle and square are same. 

∴`3(x+4)xx x=(x+4)^2` 

⇒`3x^2+12x=(x+4)^2` 

⇒`3x^2+12x=x^2+8x+16` 

⇒`2x^2+4x-16=0` 

⇒`x^2+2x-8=0` 

⇒`x^2+(4-2)x-8=0` 

⇒`x^2+4x-2x-8=0` 

⇒`x(x+4)-2(x+4)=0` 

⇒`(x+4)(x-2)=0` 

⇒`x=-4  or  x=2` 

∴ `x=2`                      ( ∵The value of x cannot be negative)  

Thus, the breadth of the rectangle is 2 cm and length is  `{3(2+4)=18}` 

Also, the side of the square is 6 cm.