Question 688745
Let X = the length of a side on the small square.
Let Y = the length of a side on the large square.

The area of a square is the Length^2

Equation 1: {{{X^2 + Y^2 = 89}}}
Equation 2: {{{X + 3 = Y}}}
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Substitute (X + 3) into equation 1 for Y.
Equation 1: {{{X^2 + Y^2 = 89}}}
{{{X^2 + (X + 3)^2 = 89}}}
Rewrite the equation
{{{X^2 + (X+3)*(X+3) = 89}}}
Simplify the equation
{{{X^2 + X^2 + 3X + 3X + 9 = 89}}}
Combine like terms
{{{2X^2 + 6X + 9 = 89}}}
Subtract 89 from bith sides
{{{2X^2 + 6X - 80 = 0}}}
Use the quadratic equation.

*[invoke quadratic "X", 2, 6, -80]

Note that you can not have a negative value for the answer. So X = 5
Now plug 5 into equation 2 for X
Equation 2: {{{X + 3 = Y}}}
{{{5 + 3 = Y}}}
{{{highlight(8 = Y)}}}

So the two sides are 5cm & 8cm