The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the
squares is 65 in squared . Find the lengths of the sides of the two squares.
2 answers:
Answer:

And 
Step-by-step explanation:
For this case we assume that for the first square we have the following dimensions:

And we know that:

And the area for the second square would be:

And we know that the sum of areas is 65 so then we have this:

And replacing we got:


We can divide the last expression by 2 and we got:

And we can factorize the last expression like this:

And we have two solutions for
and we got:

Since the length can't be negative we have this:

And 
Answer:
4 inch and 7 inch
Step-by-step explanation:
Let the length of the smaller square=l
Since the length of each side of a square is 3 in. more than the length of each side of a smaller square,
Length of the bigger square=l+3
Area of Smaller Square=l²
Area of Larger Square=(l+3)²
The sum of their areas is 65 inch squared
Therefore: l²+(l+3)²=65
l²+(l+3)(l+3)=65
l²+l²+3l+3l+9=65
2l²+6l+9-65=0
2l²+6l-56=0
2l²+14l-8l-56=0
2l(l+7)-8(l+7)=0
(2l-8)(l+7)=0
2l-8=0 or l+7=0
l=4 or -7
l= 4 inch
The length of the larger square is (4 +3) inch =7 inch
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