Find the exact value of x.

x=

6.73

Step-by-step explanation:

Remark

There might be an easier way to do this problem. I'm certain I don't know what it is. Begin by called WY = y

Givens

WY = y

WZ = x

XW = 25 - y

XZ = 24

YZ = 7

Equations

x^2 + y^2 = 7^2

(25 - y)^2 + x^2 = 24^2

Solution

x^2 = 7^2 - y^2

x^2 = 24^2 - (25 - y)^2

Since both xs are the same, you can equate the right side of the equations.

7^2 - y^2 = 24^2 - (25 - y)^2                 Expand the brackets

7^2 - y^2 = 24^2 - (625 - 50y + y^2)    Remove the brackets.

7^2 - y^2 = 576 - 625 + 50y - y^2        Cancel the y^2. Combine 576 and 625

49  = - 49 + 50y                                    Add 49 to both sides

98 = 50y                                               Divide by 50

y = 1.96

Now use y to find x

x^2 + y^2 = 7^2

x^2 = 7^2 - 1.96^2

x^2 = 45.1584

x = 6.72

9514 1404 393

  x = 6.72

Step-by-step explanation:

The triangles are all similar, so the ratios of corresponding sides are the same.

  short leg/hypotenuse = 7/25 = x/24

  x = 24(7/25)

  x = 6.72

- 70

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