Each side of a square is increased 4 inches. When this happens, the area is multiplied by 9. How many inches in the side of the original square?

Question

Each side of a square is increased 4 inches. When this happens, the area is multiplied by 9. How many inches in the side of the original square?

Answer 1

Let X = length of each one of the ORIGINAL four sides of the square

Let the AREA of the ORIGINAL SQUARE = X²

The SIDE LENGTH of the NEW SQUARE is X + 4.

The AREA of the NEW SQUARE is 9 times that of the ORIGINAL SQUARE = 9X²

(X + 4)² = 9X²

X² + 8X + 16 = 9X²

-8X² + 8X + 16 = 0

8X² - 8X - 16 = 0 Multiplying entire equation by -1.

X² - X - 2 = 0 Dividing entire equation by 8.

(X - 2) (X + 1) = 0 Factoring

X - 2 = 0 AND X + 1 = 0 which means X = -1 and we can't have a negative inch.

X = 2

ANSWER: ORIGINAL SQUARE WHERE EACH SIDE IS 2 INCHES IN LENGTH.

CHECKING:

Original Square AREA: 2 x 2 = 4 square inches

New Square AREA: 6 x 6 = 36 square inches which is 9 times more area than

the original.

Hope this was helpful RALPH.

Answer 2

Alright, let's break this up:

So, we know the original square has a side length, s. All the sides have a length s since it is a square.

By geometry, a square's area is equal to the square of its side length. This will be our first equation. We'll call the original square Square 1, where

A₁ = s² (Equation 1)

When the square's side length is increased by 4 inches, this became a new square with an area 9 times bigger than the area of square 1. We will call this square 2. We will relate the areas like so:

A₂ = (4+s)²

A₂ = 9 * A₁

A₂ = 9 * s²

Now we can take these three equations above, and relate the two areas to solve for s:

9s² = (4+s)² (Equation 2)

You will want to use the distributive rule, moving everything to one side so that the other side is equal to 0, and using the quadratic formula to solve for s. Hint: the value of s you should choose should not be a negative number! When you get your answer for s, plug it into equation 2 and see if both sides are equal.If they are, you will know that you have found the correct side length of the original square.