Answer:
24/7 = 3 3/7 inches
Step-by-step explanation:
The triangle can be represented by a line in the first quadrant with y-intercept 8 and x-intercept 6. Then its equation is ...
x/6 +y/8 = 1 . . . . . intercept form of the equation of the line
4x + 3y = 24 . . . . multiply by 24 to get standard form
Since the square will have the origin as one corner, and all sides are the same length, the opposite corner will lie on the line y=x. Then we're solving the system ...
4x +3y = 24
y = x
to find the side length.
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By substitution for y, this becomes ...
4x +3x = 24
7x = 24
x = 24/7 = 3 3/7
The length of the side of the square is 3 3/7 inches.
