Find the length of the segment indicated. A. 16.4 B. 11.4 C. 12.1 D. 13.3

Mathematics

1 answer:

kykrilka [37]2 years ago

4 0

using Pythagorean triplet

$\\ \sf\longmapsto P^2=H^2-B^2$

$\\ \sf\longmapsto x^2=19.6^2-15.4^2$

$\\ \sf\longmapsto x^2=384.16-237.16$

$\\ \sf\longmapsto x^2=147$

$\\ \sf\longmapsto x=\sqrt{147}$

$\\ \sf\longmapsto x=12.1$

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Can someone please explain how the answer is D

Kitty [74]

Step-by-step 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:

${c}^{2} = {x}^{2} + {y}^{2} \\ {c}^{2} = {8}^{2} + {17}^{2} = 64 + 289 \\ {c}^{2} = 353 \\ c = \sqrt{353}$