Answer:
1. x = 4
This is a 45-45-90 triangle, which means the measurements would follow the ratio: 1 - 1 - √2. Note that √2 is given to you (4√2). Divide √2 from the number given:
(4√2)/(√2) = 4
x = 4
2. x = 3√2
Again, it is a 45-45-90 triangle, only this time, one of the side measurements are given to you. Solve for the hypotenuse by multiplying √2. 3 x √2 = 3√2.
3. 5√2
As explained on top, the side measurements are 1 , 1, √2. The 1 side is given to you (5). Multiply by √2. 5 x √2 = 5√2.
4. x = √3 ; y = 2
Note that the measurements of a 30-60-90 triangle are 1, √3, and 2. Since the shortest side is 1, just fill in the blanks with the rule.
5. The second shortest side is given to you (4√3). Divide by √3
4√3/(√3) = 4
Shortest side: 4
4 x 2 = 8
Hypotenuse: 8
6. 10 is the hypotenuse, you are solving for the two shorter sides.
10/2 = y
y = 5
5 x √3 = x
x = 5√3
7. You must use the 1, 1, √2 formula, in which 11 is √2.
Divide:
11/√2 = 7.778
Now, find the area. It is a square, and so, multiply 7.778 with 7.778 (A = s²)
A = 7.778² = 60.50 m² (rounded).
8. Note that each side length is 20, therefore, this is an equilateral triangle.
To solve, use the formula (x√3)/2 :
x = 20
Plug in 20 for x:
(20√3)/2 = 10√3
10√3 yd is your height.
Now solve for area. The area of a triangle can be solved using: A = (1/2)bh
A = (1/2)(20)(10√3)
A = (10)(10√3)
A = 100√3 yd²
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