Question

What is the length of x, in simplest exact form?

a) 14
b) 144
c) 12
d) 144
e) 194

Answer 1

The length of the straight-line distance can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the eastward distance is 9 blocks and the northward distance is 5 blocks. Thus, the length of x, in simplest exact form, is √2√53.

Step-by-step explanation:

The length of the straight-line distance can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the eastward distance is represented by the base of the triangle (9 blocks) and the northward distance is represented by the height of the triangle (5 blocks).

Using the Pythagorean theorem, we can find the length of the hypotenuse (x) as follows:

1. Square the length of the base: 9^2 = 81
2. Square the length of the height: 5^2 = 25
3. Add the squared lengths of the base and height: 81 + 25 = 106
4. Take the square root of the sum: √106 = √(2*53) = √2 √53

Therefore, the length of x, in simplest exact form, is √2 √53. None of the given options (a) 14, (b) 144, (c) 12, (d) 144, (e) 194 match this answer, so the correct answer is not listed.