Question

a square has a side length of x. A rectangle has a length that is 4 inches longer than the square and a width that is 2 inches shorter than the square. If the areas of the square and rectangle are equal, what is the length of the rectangle?

Answer 1

Answer:

Length of the rectangle is = 8 inches.

Step-by-step explanation:

Given :

Area of square = Area of the rectangle

According to the question:

Length of the square be 'x'.

Its area = (Side)*(Side) =$x^2$   ...equation (i)

Length of the rectangle = $(x+4)$

Width of the rectangle = $(x-2)$

Area of the rectangle =Length * Width

⇒$(x+4)(x-2)=x^2-2x+4x-8$

⇒$x^2+2x-8$          ...equation  (ii)

Equating both the equation as area of both the figure are equal.

⇒ $x^2+2x-8=x^2$

⇒ $2x-8=0$     ...subtracting $x^2$ both sides

⇒ $2x=8$           ...dividing both sides with 2

⇒ $x=\frac{8}{2}=4$ inches

Plugging the value of x=4 in the length of the rectangle.

We have,

⇒$(x+4)=(4+4)=8$

So the length of the rectangle = 8 inches.