Question

One side of a square was reduced by 3 in and the other side was enlarged by 11
inches. The area of a resulting rectangle is 15 inches squared.
Find the side of the square.

Answer 1

Answer:

Each side of the square is 4 inches long

Step-by-step explanation:

Original side: x

(x-3)*(x+11)=15

x^2 + 8x - 48 = 0

If you solve the equation your answer would by x=4 inches.

Answer 2

Applying the formula of area of a rectangle, the side of the square is calculated as: 4 inches.

What is the Area of a Rectangle?

Area of rectangle = length × width

Thus, the dimensions of the resulting rectangle would be as follow:

let x represent the side of the square.

Width = x - 3

Length = x + 11

Area of rectangle = 15 sq. in.

Therefore:

(x - 3)(x + 11) = 15

x² + 11x - 3x - 33 = 15

x² + 8x - 33 - 15 = 0

x² + 8x - 48 = 0

Factorize

(x - 4)(x + 12) = 0

x = 4 or x = -12

The side of the square cannot be negative, therefore, the side of the square is: 4 inches.

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