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fiasKO [112]
3 years ago
14

Triangle ABC had a perimeter 18 cm

Mathematics
1 answer:
Alex3 years ago
4 0

Step-by-step explanation:

what is the main condition the lengths of the sides of a right-angled triangle have to fulfill ?

Pythagoras !

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90 degree angle), a and b are the so-called legs (the sides enclosing the 90 degree angle).

only if there is a combination of the sides, for which the Pythagoras equation is true, do we have a right-angled triangle. otherwise not.

we also know CA = 18 - 7 - 3 = 8 cm

so, let's try

8² = 7² + 3²

64 = 49 + 9 = 58 wrong

7² = 8² + 3²

49 = 64 + 9 = 73 wrong

3² = 8² + 7²

9 = 64 + 49 = 113 wrong

so, there is no combination, where the Pythagoras equation is true, so it is NOT a right-angled triangle.

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PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
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-2<em>x</em> + 6<em>y</em> = -38

3<em>x</em> - 4<em>y</em> = 32

To solve by elimination, multiply the top equation by 3 and the bottom equation by 2.

3(-2<em>x</em> + 6<em>y</em> = -38) --> -6<em>x</em> + 18<em>y</em> = -114

2(3<em>x</em> - 4<em>y</em> = 32) --> 6<em>x</em> - 8<em>y</em> = 64

Add the equations.

-6<em>x </em>+ 18<em>y</em> = -114

6<em>x</em> - 8<em>y</em> = 64

+_____________

0 + 10<em>y</em> = -50

10<em>y</em> = -50

<em>y</em> = -5

Substitute -5 for y into one of the original equations to find x.

3<em>x</em> - 4<em>y</em> = 32

3<em>x</em> - 4(-5) = 32

3<em>x</em> + 20 = 32

3<em>x</em> = 12

<em>x</em> = 4

Check work by plugging the <em>x</em>- and <em>y</em>-values into both of the original equations.

-2<em>x</em> + 6<em>y</em> = -38

-2(4) + 6(-5) = -38

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38 = 38


3<em>x</em> - 4<em>y</em> = 32

3(4) - 4(-5) = 32

12 + 20 = 32

32 = 32

Answer:

<em>x</em> = 4 and <em>y</em> = -5; (4, -5).

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