Find the values of x and y. Show all of your calculations and an explanation of how you used geometry concepts to determine the method you used.

Question

Find the values of x and y. Show all of your calculations and an explanation of how you used geometry concepts to determine the method you used.

 

WRITER

Answer 1

the only geometry concept is pythagorean theorem used three time.

Label PR as z

3²+y²=x²

24²+y²=z²

adding 2y²=x²+z²-24²-3²

also x²+z²=27²

so y²=27²-24²-3²=72, y= square root 72

x²=72+9, x=9

Answer 2

Review the Triangle Geometric Mean Theorem. The altitude, y, is equal to the geometric mean of QS (= 3) and RS (= 24):

y = √(QS·RS) = √(3·24) = √72 = √(36·2) = 6√2

To find x, apply the Pythagorean Theorem on triangle PQS.