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

Answers ( )

    0
    2021-10-08T06:25:53+00:00

    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

    0
    2021-10-08T06:26:05+00:00

    Answer:

     L_1 = 4

    And  L_2 = 3 +4 = 7

    Step-by-step explanation:

    For this case we assume that for the first square we have the following dimensions:

     A_1 = L^2_1

    And we know that:

     L_2 = 3 + L_1

    And the area for the second square would be:

     A_2 = L^2_2 = (3+L_1)^2 = 9 + 6L_1 + L^2_1

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

     A_1 + A_2 = 65

    And replacing we got:

     L^2_1 + 9 + 6L_1 + L^2_1 = 65

     2L^2_1 +6L_1 - 56=0

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

     L^2_1 + 3L_1 -28=0

    And we can factorize the last expression like this:

     (L_1 + 7) (L_1 -4) =0

    And we have two solutions for  L_1 and we got:

     L_1 = 4, L_1 = -7

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

     L_1 = 4

    And  L_2 = 3 +4 = 7

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