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Radda [10]
3 years ago
10

find x. assume that segments that appear tangent are tangent. please help need answer and how to do it.

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
3 0
Triangle ABC is a right triangle, meaning we can use the Pythagorean Theorem to find x.
The formula for the Pythagorean Theorem is:
a =  \sqrt{ {b}^{2}  +  {c}^{2} }
where a is the hypotenuse, and b and c are the legs.
In this problem, we have the vertical leg as 16, the horizontal leg as x, and the hypotenuse as 20. Therefore, we can say that
a = 20 \\ b = 16 \\ c = x
Therefore, we can plug into the formula to find x:a =  \sqrt{ {b}^{2}  +  {x}^{2} }  \\  {a}^{2}  =  { \sqrt{ {b}^{2}  +  {x}^{2} } }^{2}  \\  {a}^{2}  =  {b}^{2}  +  {x}^{2}  \\  {a}^{2}  -  {b}^{2}  =  {x}^{2}
We first change the variable c to x and square both sides of the equation. Then we subtract b^2 from both sides.
{x}^{2}  =  {a}^{2}  -  {b}^{2}  \\  \sqrt{ {x}^{2} }  =  \sqrt{ {a}^{2}  -  {b}^{2} }  \\ x =  \sqrt{ {a}^{2} -  {b}^{2}  }
We square root each side to find the variable answer for x. Then we plug in the numbers:x =  \sqrt{ {(20)}^{2} -  {(16)}^{2}  }  \\ x =  \sqrt{400 - 256}  \\ x =  \sqrt{144}  \\ x = 12
We find that x = 12. The answer is A. 12.
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