Question

the length and width of a rectangle are (x+4) cm and x cm respectively. A square has the same perimeter as this rectangle . if you add the areas of the rectangle and the square , the result is 94 cm^2. Solve for x.

Answer 1

We know that the length of any rectangle is length times width. So, the area of the rectangle would be x(x+4). Its perimeter would be x+x+(x+4)+(x+4) or 4x+8. The perimeter of the rectangle is the same as the perimeter of the square: 4x + 8. Since all 4 sides of a square are equal, we can divide the perimeter of the square by 4 to get the expression of one side. (4x+8)/4 = x+2. So, the area of the square is (x+2)(x+2). We now know the areas of both the rectangle and the square, so now we set up the equation: x(x+4) + (x+2)(x+2) = 94.

$x^{2} + 4x + x^{2} + 4x + 4 = 94$
$2x^{2} + 8x + 4 - 94 = 0$
$x^{2} + 4x -45 = 0$

(x+9)(x-5) = 0
x= -9, 5
x=5 (Because you cannot have a negative value for a length)