Question

Can someone please explain how the answer is D

Answer 1

Explanation:

Because the length of ST is calculated using pythagorean theorem:

`{c}^(2) = {a}^(2) + {b}^(2)`

Where the square of the hypotenuse is equal to the sum of squares of the other two sides of a right triangle. In this case, the hypotenuse is ST and the other two sides are distances between S and T over the X and Y axis. Those are easily calculated:

`x = |sx - tx| \\ y = |sy - ty|`

Where x is the distance between S and T over X axis and Y distance over Y axis, sx and tx are X coordinates of S and T, sy and ty are Y coordinates of S and T.

Using that formula, you get that y = 17 and x = 8.

Back to the pythagorean theorem, if we put those number in the formula of the pythagorean theorem, we get something like this:

`{c}^(2) = {x}^(2) + {y}^(2) \\ {c}^(2) = {8}^(2) + {17}^(2) = 64 + 289 \\ {c}^(2) = 353 \\ c = √(353)`

And finally, the correct answer is in fact 353.