Chapter 8.7, Problem 32PPS

To determine

To find: The length of the square of which the area is represented by given expression.

Answer to Problem 32PPS

The length of each side of square is $3x-7$ .

Explanation of Solution

Given information:

The area of the square is represented by the expression $9x^2-42x+49$ .

Concept used:

The expression representing the area of a square should be a perfect square.

Calculations:

The area of the square is represented by the quadratic expression $9x^2-42x+49$ .

The factors of the expression $9x^2-42x+49$ represent the length and width of the square.

Now, $9x^2-42x+49={\left(3x\right)}^2-2\cdot \left(3x\right)\cdot \left(7\right)+{\left(7\right)}^2$

  $\Rightarrow 9x^2-42x+49={\left(3x-7\right)}^2$

  $\Rightarrow 9x^2-42x+49=\left(3x-7\right)\times \left(3x-7\right)$

Length of the square = $3x-7$ . Width of the square = $3x-7$

Thus, the length of each side of square is $3x-7$ .

Conclusion:

The length of each side of square is $3x-7$ .