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3 years ago

Which dimensions cannot create a triangle?

2 answers:

7 0

Angles that create a triangle always add up to 180.

To find sides that create triangles, we have to use the Triangle Inequality Theorem.
It's where side A + B will always be greater than side C
and B + C will always be greater than side A
and A + C will always be greater than side B.

So let's check all of these answers and pick the one that's incorrect.

A.
10 + 25 + 145 = 180?
Correct!

B.
9 + 15 > 9?
Correct!
15 + 9 > 9?
Correct!
9 + 9 > 15?
Correct!

C.
40 + 70 + 60 = 180?
Incorrect! 40 + 70 + 60 = 175 which is less than 180.

The answer is three angles measuring 40 m, 70 m, and 60 m.

Hope this helped! If you have anymore questions or don't understand, please comment or DM me. :)

Papessa [141]3 years ago

3 0

For a triangle to be "true", it must either have angle measures that total to 180 degrees or have two sides whose sum is greater than the third side.

For the first one, the angles total to 180 (10+25=35 and 145+35=180). This is a good triangle.

In the second one, the two shorter sides are 9 and 9. Adding these up, we get a sum of 18, and since this is greater than 15 (the third side), this triangle is also good.

The third triangle has angle measures that equal 175. Since it is less than 180 degrees, this is not a good triangle.

Finally for the fourth one, we see that the two shorter sides are 6 and 8. Their sum is 14, and since this is greater than 10, this is a good triangle.

So our third option is the one that cannot create a triangle.

:)

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3 years ago

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Answer:

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Answer:

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faltersainse [42]

Answer:

4(k - 3)(3k + 5)

Step-by-step explanation:

Given

12k² - 16k - 60 ← factor out 4 from each term

= 4(3k² - 4k - 15) ← factor the quadratic

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vredina [299]

Answer:

Around 5.5 square meters

Step-by-step explanation:

You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula $\frac{1}{3} \pi r^2 =3\pi$ square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is $\sqrt{3}$ times larger than the smaller leg. In this case, these dimensions are a base of $\frac{3}{2}$ for the smaller leg and $\frac{3\sqrt{3}}{2}$ for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get $\frac{9\sqrt{3}}{4}$ square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!

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