SOLUTION: If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square. The length of the original square is ? cm.

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Question 223191: If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square.
The length of the original square is ? cm.

Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
If the sides of a square are lengthened by 8 cm, the area become 256cm^2. Find the length of the original square.

The length of the original square is ? cm.

Step 1. Let x be the length of the original side of the square.

Step 2. Let x+8 be the length having an area of 256 square centimeters.

Step 3. Area A=(x+8)^2=256 since the area of the square is the square of its side x+8.

Step 4. Solving equation in Step 3 yields the following steps:



Subtract 256 from both sides of the equation





Step 5. To solve, use the quadratic formula given as



where a=1, b=16, and c=-192.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1024 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -24. Here's your graph:



Choosing the positive solution x=8. Note

Step 6. ANSWER: The length of the side of the original square is 8 cm.


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J





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