## 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 6

Question

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.

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6 days 2021-10-08T06:24:51+00:00 2 Answers 0

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 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 