SOLUTION: Right triangle ABC has one leg of length 6 cm, one leg of length 8 cm and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the tw

Question 1143715: Right triangle ABC has one leg of length 6 cm, one leg of length 8 cm and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square, in cm? Express your answer as a common fraction.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let the square be DEFG, with DE on hypotenuse BC, F on AC, and G on AB.

Triangle ABC is a 3-4-5 right triangle; since DEFG is a square, triangles AFG, EFC, and DBG are also right triangles with side lengths in the ratio 3:4:5.

So if x is the side length of the square, then
(1) AF:GF = AF:x = 3:5
(2) FC:FE = FC:x = 5:3

Use those proportions to get the lengths of AF and FC in terms of x; then use

AF+FC = AC = 8

to solve for x.
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