a - length of side of a square
t - length of side of a triangle
The perimeter of a square: 
The perimeter of a triangle: 
We have the area of a triangle: 
The formula of an area of an equilateral trinagle: 
Substitute:
<em>multiply both sides by 4</em>
<em>divide both sides by 
</em>
The perimeter of a triangle: 
Substitute to the formula of a perimeter of a square:
<em>divide both sides by 4</em>
The formula of a diagonal of a square: 
Substitute:
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
Answer:
A. 6 m by 6 m
Step-by-step explanation:
You can try the different choices to see which has the largest area. Of course, the area is the product of the dimensions:
6 m × 6 m = 36 m² . . . . largest area
10 m × 2 m = 20 m²
8 m × 4 m = 32 m²
__
The largest area is that of a square, 6 m by 6 m. (choice A)
Answer:
Step-by-step explanation:
Notice that the series: 1 - 3 + 9 - 27 +... clearly has powers of the factor 3 in its terms and it is also an alternate series (the terms alternate from positive to negative). The terms are positive for 
(even terms) , while the odd terms 
are negative. (so most likely there should be a factor (-1) in the common ratio.
We can then represent it with the following summation expression:
given that each of its first four terms are:
