(a) One unique triangle. This is an equilateral triangle since all sides are the same length. Through the SSS property, we can prove that only one triangle is possible here.
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(b) Cannot make a triangle. The triangle inequality theorem says that adding any two sides of a triangle must result in a value larger than the third side. Add up the first two sides (1 and 2) to get 1+2 = 3, which is not larger than the third side (3 units long). I recommend cutting out strips of paper that are 1 inch, 2 inches and 3 inches long, and trying to form a triangle. You'll find that a triangle is not possible. The 1 inch and 2 inch strips will line up to form a straight line that is 3 inches long, and basically you have a flat line (or a triangle with area 0)
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(c) More than one triangle. The angles add up to 180 since 35+60+85, so we can form a triangle. It turns out we can form infinitely many of them. The AA (angle angle) similarity theorem allows us to scale any triangle to make it larger or smaller compared to the original.
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(d) Cannot make a triangle. I'm assuming the 509 should actually be 50°. If so, then a triangle is not possible because the three angles (50, 50, 50) do not add to 180. We have instead 50+50+50 = 150. For any triangle, the three angles must always add to 180 degrees.
Answer:
What is meant by galons and quarts?
Step-by-step explanation:
Say me the meaning and I will answer it.
Answer:
D : 510 units
Step-by-step explanation:
NOTE:
Something to consider when solving problems like this is to break the large shape down into smaller, more managable shapes. So for this problem, you can break down this irregular shape into two rectangles. This will make solving problems similar to this easier in the future :)
WORK:
I broke down this shape into two rectangles with the following dimensions:
- 12 meters by 5 meters
- 3 meters by 14 meters
You also know that the depth has to be 5 feet (the problem itself did not account for differences in feet and meters, as when I converted the 5 feet to meters and solved that way, none of the answers were correct)
Using this information, you can now solve for the volume of each of the rectangles
12*5*5 = 300 units
3*14*5 = 210 units
Then, you simply add the two volumes together to find the total volume needed to fill the pool which equals
510 units
4.2 because it has a box around the corner that makes it whole
