Question

Please help problem 3 and 4show workfind the value of x, y and z​

Answer 1

Answer:

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle create two smaller triangles, all of which are similar to the original. This means corresponding sides are proportional.

3. Using the above relationship, ...

short-side/hypotenuse = 8/y = y/(8+23)

y^2 = 8·31

y = 2√62

__

long-side/hypotenuse = z/(8+23) = 23/z

z^2 = 23·31

z = √713

__

short-side/long-side = 8/x = x/23

x^2 = 8·23

x = 2√46

_____

4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,

y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)

z = √(20·25) = 10√5 . . . . . = √(long segment × hypotenuse)

x = √(5·20) = 10 . . . . . . . . . = √(short segment × long segment)