SOLUTION: If the sides of a square are lengthened by 6cm the area becomes 169cm^2. Find the length of a side of the original square? I do so have a tough time deciphering word problems, and

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: If the sides of a square are lengthened by 6cm the area becomes 169cm^2. Find the length of a side of the original square? I do so have a tough time deciphering word problems, and      Log On


   

Question 163887: If the sides of a square are lengthened by 6cm the area becomes 169cm^2. Find the length of a side of the original square?
I do so have a tough time deciphering word problems, and need some help please.
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= the side of the original square in cm
The problem says
%28x+%2B+6%29%2A%28x+%2B+6%29+=+169 cm2
or
%28x+%2B+6%29%5E2+=+169
Take the square root of both sides
x+%2B+6+=+13
x+=+7
The side of the original square is 7 cm
check:
%28x+%2B+6%29%2A%28x+%2B+6%29+=+169 cm2
%287+%2B+6%29%2A%287+%2B+6%29+=+169 cm2
13%2A13+=+169
169+=+169
OK

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Area of original square:

A=s%5E2 where A is the area and s is the side length


Since "the sides of a square are lengthened by 6cm the area becomes 169cm^2", this means that we replace A with 169 and s with s%2B6 to form the area of the enlarged square. So we get:

169=%28s%2B6%29%5E2


169=s%5E2%2B12s%2B36 FOIL


0=s%5E2%2B12s%2B36-169 Subtract 169 from both sides


0=s%5E2%2B12s-133 Combine like terms.


Notice we have a quadratic equation in the form of as%5E2%2Bbs%2Bc where a=1, b=12, and c=-133


Let's use the quadratic formula to solve for s


s+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


s+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%281%29%28-133%29+%29%29%2F%282%281%29%29 Plug in a=1, b=12, and c=-133


s+=+%28-12+%2B-+sqrt%28+144-4%281%29%28-133%29+%29%29%2F%282%281%29%29 Square 12 to get 144.


s+=+%28-12+%2B-+sqrt%28+144--532+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-133%29 to get -532


s+=+%28-12+%2B-+sqrt%28+144%2B532+%29%29%2F%282%281%29%29 Rewrite sqrt%28144--532%29 as sqrt%28144%2B532%29


s+=+%28-12+%2B-+sqrt%28+676+%29%29%2F%282%281%29%29 Add 144 to 532 to get 676


s+=+%28-12+%2B-+sqrt%28+676+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


s+=+%28-12+%2B-+26%29%2F%282%29 Take the square root of 676 to get 26.


s+=+%28-12+%2B+26%29%2F%282%29 or s+=+%28-12+-+26%29%2F%282%29 Break up the expression.


s+=+%2814%29%2F%282%29 or s+=++%28-38%29%2F%282%29 Combine like terms.


s+=+7 or s+=+-19 Simplify.


So the possible answers are s+=+7 or s+=+-19


However, since a negative length isn't possible, this means that the only answer is s=7