Answer:
Refer to step-by-step.
Step-by-step explanation:
12. x = 28
BC = x
AB = 96
AC = 100
We use the Pythagorean theorem to find the value of x.
a² + b² = c²
x² + 96² = 100²
x² + 9216 = 10000
x² = 10000-9216
x² = 784
√x² = √784
x = 28
13. x = 64
a² + b² = c²
48² + x² = 80²
2304 + x² = 6400
x² = 6400 - 2304
x² = 4096
√x² = √4096
x = 64
14. YES and 25 = 25
a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
So this means that AB is tangent to the circle.
15. NO and 45 ≠ 49
a² + b² = c²
3² + 6² = 7²
9 + 36 = 49
45 = 49
So this means the AB is not tangent to the circle.
16. x = 4.5 and P = 52
To find the value of x, we need to determine the value of our hypotenuse.
QU is congruent to QT, therefore, QT = 4
UR is congruent with SR, therefore, UR = 13
PS is congruent to AB, therefore:
2x = 9
Divide both sides by 2
x = 4.5
The perimeter of a triangle is:
P = a + b + c
a = 9 + 4 or 13
b = 2(4.5) + 13 or 22
c = 4 + 13 or 17
P = 13 + 22 + 17
P = 52
17. x = 13 and P = 72
TJ is congruent to UJ, therefore, TJ = 13
x = 13
The perimeter of a parallelogram is:
P = 2(a+b)
a = HR + RK
b = KU + UJ
a = 13 + 5 or 18
b = 5 + 13 or 18
P = 2(18 + 18)
P = 2(36)
P = 72
18. x = 8 and P = 80
We know that part of the whole of 26 is 18 because one side is congruent to 18.
to find the value of the other half, we simply subtract 18 from 26.
26 - 18 = 8
x is congruent to 8, therefore x = 8
The line segment 14 is congruent to the opposite segment of x, therefore making the value 14.
So then we have:
a = 8 + 14 or 22
b = 26
c = 18 + 14 or 32
P = a + b + c
P = 22 + 26 + 32
P = 80
19. x = 6 and P = 52
Now we have the case of x + 2 is congruent to 8.
x + 2 = 8
Combine like terms.
x = 8 - 2
x = 6
Now that we have the value of x, we can simply look for the value of the line segment attached to it.
4 is congruent to the line segment attached to x + 2, therefore the value is 4.
To find the perimeter we have to add all sides together.
P = (8+5)+(5+9)+(9+4)+(8+4)
P = 52
20. x = 5, y = 2, z =10, and P = 68
Let's take this one step at a time.
First we look for x.
2x + 2 = 3x - 3
Combine like terms.
2x - 3x = -3 - 2
-x = -5
Divide both sides by -1.
x = 5
Now let's get the value of y.
5y - 2 = 3y + 2
Combine like terms.
5y - 3y = 2 + 2
2y = 4
Divide both sides by 2.
y = 2
Now let's look for z.
34 - 2z = z + 4
Combine like terms.
-2z - z = 4 - 34
-3z = -30
Divide both sides by -3.
z = 10
Now that we have the values of x, y, and z. We can substitute them to find the values of our segments.
2x + 2
2(5) + 2 = 12
3x - 3
3(5)-3 = 12
5y - 2
5(2) - 2 = 8
3y + 2
3(2) + 2 = 8
z + 4
10 + 4 = 14
34 - 2z
34 - 2(10)
34 - 20 = 14
Now that we have our values let's look for our perimeter.
P = a + b + c
P = (12 + 8) + (12 + 14) + (14 + 8)
P = 20 + 26 + 22
P = 68
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