Chapter 9, Problem 52SGR

To determine

To compute the side of the square.

Answer to Problem 52SGR

The side of the square is 12 feet.

Explanation of Solution

Given information :

The side of the square is quadrupled if the length and breadth is increased by 4 inches.

Formula used :

Area of a square is given by $a=x^2$ . Where ‘a’ is the are and ‘x’ is the breadth.

Once the two separate areas are found out, equate the areas to compute the side of the square. Use factorization of a quadratic equation to solve the same.

Calculation :

  $a=x^2$

Let this be equation 1. This is the area of the original square.

  $4a={\left(x+4\right)}^2$

Let this be equation 2. This is the new area of the square, as per the given information.

  $4x^2={\left(x+4\right)}^2$

Putting the value of ‘a’ of equation 1 in equation 2.

  $=>4x^2=x^2+8x+16$

Simplifying the equation.

  $=>4x^2-x^2-8x-16=0$

Arranging this is a quadratic equation form.

  $=>3x^2-8x-16=0$

Factorize this to get the length.

  $=>3x-12x+4x-16=0$

Breaking the middle term.

  $=>3x\left(x-12\right)+4\left(x-12\right)=0$

Arranging the common terms

  $=>\left(3x+4\right)\left(x-12\right)=0$

These are the factors of the equation.

  $=>x=-\frac{4}{3};12$

Since the length of the square cannot be a negative value, the length is 12 feet.