Using the Pythagorean Theorem, it is found that the length of the dotted line in the diagram below is of 8.6 units.
What is the Pythagorean Theorem?
The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In this problem:
- The length of the dotted line is the hypotenuse of a right triangle with legs 7 and x.
- x is the hypotenuse of a right triangle with sides 3 and 4.
Hence, the value of x is found as follows.
[tex]x^2 = 3^2 + 4^2[/tex]
[tex]x^2 = 25[/tex]
[tex]x = \sqrt{25}[/tex]
[tex]x = 5[/tex]
Then, the length l of the dotted line is found as follows.
[tex]l^2 = 5^2 + 7^2[/tex]
[tex]l = \sqrt{74}[/tex]
[tex]l = 8.6[/tex]
The length of the dotted line in the diagram below is of 8.6 units.
To learn more about the Pythagorean Theorem, you can take a look at https://brainly.com/question/654982
