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) About Me  (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:

%28x%2B8%29%5E2=x%5E2%2B16x%2B64=256

Subtract 256 from both sides of the equation

x%5E2%2B16x%2B64-256=256-256

x%5E2%2B16x-192=0

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

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

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

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B16x%2B-192+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2816%29%5E2-4%2A1%2A-192=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+1024+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%2816%29-sqrt%28+1024+%29%29%2F2%5C1+=+-24

Quadratic expression 1x%5E2%2B16x%2B-192 can be factored:
1x%5E2%2B16x%2B-192+=+1%28x-8%29%2A%28x--24%29
Again, the answer is: 8, -24. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B16%2Ax%2B-192+%29



Choosing the positive solution x=8. Note %288%2B8%29%5E2=256

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