Question 694543

The side of one square is 3 cm longer than the side of another square. If the sum of the area of the 2 squares is 65 centimetres squared find the lengths of each square.

Can you please help me? thanks in advance


Let one side of smaller square be S


Then one side of larger square = S + 3


Area of smaller square = S(S), or {{{S^2}}}


Area of larger square = (S + 3)(S  + 3), or {{{(S + 3)^2}}}, or {{{S^2 + 6S + 9}}}


Since sum of areas of the 2 squares = 65, then: {{{S^2 + S^2 + 6S + 9 = 65}}}


{{{2S^2 + 6S + 9 - 65 = 0}}}


{{{2S^2 + 6S - 56 = 0}}}


{{{2(S^2 + 3S - 28) = 2(0)}}}


{{{S^2 + 3S - 28 = 0}}}


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


S = - 7 (ignore)


S, or length of ones side of smaller square = {{{highlight_green(4)}}}
 

Length of one side of larger square = 4 + 3, or {{{highlight_green(7)}}}


You can do the check!!


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