MATH MS.SUE HELP PLEASE!
posted by bob .
Could somebody help me I don't understand any of this. Could someone show me or tell me how to work the problems?
1. Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm
A.8
B.21
C.15
D.225
2.The length of a hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the length of the other leg.
A.14
B.144
C.8
D.12
3.Which of the triangles decribed in the table are a right triangle?
Triangle  Side 1  Side 2  Side3 
Q  25  20  15 
R  26  20  14 
S  25  20  1026 
T  25  26  650 
Answer choices:
A. (Q)
B. (R)
C.(S)
D.(T)
4.Point E is located at point (2, 2) and point F is located at (4, 6). What is the distance between point E to F?
A.52 squared
B.28 squared
C.10
D.20 squared

idk how to tag so maybe this might tag Ms. Sue here.

1. a^2 +b^2 = c^2
9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2
sqrt(225) = sqrt (c^2)
c = 15
2. 5^2 +b^2 = 13^2
25 + b^2 = 169
2525 + b^2 = 16925
b^2 = 144
b= 12
3. Q
15^2 +20^2 = c^2
225 +400 =c^2
625 = c^2
c = 25
4. Sqrt (4(2)^2 + (62)^2))
Sqrt (36 + 64)
= 10 
1.
Pythagorean theorem
c = sqrt ( a ^ 2 + b ^ 2 )
c = sqrt ( 9 ^ 2 + 12 ^ 2 )
c = sqrt ( 81 + 144 )
c = sqrt ( 225 )
c = 15
Answer C
2.
Pythagorean theorem
b = sqrt ( c ^ 2  a ^ 2 )
b = sqrt ( 13 ^ 2  5 ^ 2 )
b = sqrt ( 169  25 )
b = sqrt ( 144 )
b = 12
Answer D
3.
Pythagorean theorem
c = sqrt ( a ^ 2 + b ^ 2 )
Answer A
becouse :
c = sqrt ( 20 ^ 2 + 15 ^ 2 )
c = sqrt ( 400 + 225 )
c = sqrt ( 625 )
c = 25
4.
The Distance Formula :
d = sqrt [ ( x2  x1 ) ^ 2 + ( y2  y1 ) ^ 2 ]
In this case :
x1 =  2
x2 = 4
y1 = 2
y2 =  6
d = sqrt [ ( 4  (  2 ) ) ^ 2 + ( 6  2 ) ^ 2 ]
d = sqrt [ ( 4 + 2 ) ^ 2 + (  8 ) ^ 2 ]
d = sqrt [ 6 ^ 2 + (  8 ) ^ 2 ]
d = sqrt ( 36 + 64 )
d = sqrt ( 100 )
d = 10
Answer C 
bob, You need to study the Pythagorean theorem.

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