Question

What is the length of the dotted line in the diagram below? Leave your answer in simplest radical form.

Answer 1

The length of the dotted line is √93.

Explanation:

Use Pythagorean Theorem to solve the hypotenuse of the top triangle.

8² + 5² = √89

√89 is now known as the measurement of the bottom line as well. We can visualize the dotted line as the hypotenuse of a triangle and solve for it using Pythagorean Theorem again.

√89² + 2² = √93

Answer 2

`√(93)`

Explanation:

8^2+5^2=c^2

64+25=c^2

89=c^2

c=
`√(89)` <-- this is the length of the rectangle at the bottom

2^2+(
`√(89)`)^2=c^2

4+89=c^2

c=
`√(93)` <-- length of dotted line (diagonal)