Geometry

Mathematics

1 answer:

vova2212 [387]3 years ago

7 0

X = length of third side
The third side is unknown and can't be determined to be one fixed number. However, we can find a set of values or a range of acceptable values

If we know that
a = 6
b = 7
are the two given sides, then we can say

b-a < x < b+a
7-6 < x < 7+6
1 < x < 13

So the third side x can be between 1 and 13.
The third side cannot be equal to 1 unit or 13 units because a triangle would not form. Instead a straight line would form.

Note: This idea is using the triangle inequality theorem

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Please Help!!!

Vinil7 [7]

Let's use the quadratic formula
$\frac{ - b( + - ) \sqrt{ {b}^{2} - 4ac} }{4a}$
a = 1, b = 0, c = -18
$\frac{ - (0)( + - ) \sqrt{ {(0)}^{2} - 4(1)( - 18)} } {4(1)} \\ \frac{( + - ) \sqrt{72} }{4}$
This is now split into two equations:
$\frac{ + \sqrt{72} }{4}$
and
$\frac{ - \sqrt{72} }{4}$
Since $\frac{ \sqrt{72} }{4} \\ = \frac{6 \sqrt{2} }{4} \\ = \frac{3 \sqrt{2} }{2}$
The answer is
$\frac{3 \sqrt{2} }{2} \: and \: \frac{ - 3 \sqrt{2} }{2}$
which means there are 2 real number solutions to the problem: answer B.

6 0

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