Asquare is inscribed in a right triangle so that they have a common right angle. the legs of the triangle are 6 in and 8 in long. find the length of the side of the square.

  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.

Letter a (: : : : : : : : : :

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c