SOLUTION: If the sides of a square picture frame are increased by 5 cm, the area becomes 289 cm^2. Find the length of a side of the original picture frame.

Question 100465: If the sides of a square picture frame are increased by 5 cm, the area becomes 289 cm^2. Find the length of a side of the original picture frame.
Found 3 solutions by checkley71, Earlsdon, doukungfoo:
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
(X+5)(X+5)=289
X^2+10X+25=289
X^2+10X+25-289=0
X^2+10X-264=0
(X+22)(X-12)=0
X-12=0
X=12 FOR THE ORIGINAL SIZE OF THE PICTURE
PROOF
(12+5)(12+5)=289
17*17`=289
289=289
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Let the original side length be x.Then,
Solve for x.
Subtract 289 from both sides.
Solve this quadratic equation for x by factoring.

so or
so Discard the negative solution as the side length is a positive value.
The original side length is 12 cm.
Check:

Answer by doukungfoo(195)   (Show Source): You can put this solution on YOUR website!
The area of a square is equal to one of its sides squared
OR

This problem states that if the sides of a square are increased by 5 the area becomes 289
so lets plug that information into the formula for area of a square

now just solve for s
first take the square root of both sides of the equal sign

so the sides of the original picture frame are 12 cm
Check answer

done!
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