SOLUTION: Hello, I am having a hard time solving this problem and iwas wondering if you can help me. #1 One side of a rectangle stage is 2 meters longer that the other. If the diagnonal is

Question 166306: Hello,
I am having a hard time solving this problem and iwas wondering if you can help me. #1 One side of a rectangle stage is 2 meters longer that the other. If the diagnonal is 10 meters then what is the lenghts of the sides.
#2. An angry constuction worker throws his wench downward from a height of 128 feet with am initial velocity of 32 feet per second. The height of he wrench above the ground after t seconds is given by S(t0 = 16^2-32t+ 128.
A. what is the height of the wrench after 1 second?
B. How long does it take for the wrench to reach the ground?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
#1 One side of a rectangle stage is 2 meters longer that the other. If the diagnonal is 10 meters then what is the lenghts of the sides.
.
Let x = a side of rectangle
then
x+2 = other side of rectangle
.
Applying pythagorean's theorem:
x^2 + (x+2)^2 = 10^2
x^2 + x^2+4x+4 = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x - 48 = 0
Factoring the left:
(x+8)(x-6) = 0
x = {-8, 6}
.
We can toss out negative solution since it won't make sense to have a negative length.
.
x = 6 meters
x+2 = 8 meters
.
.
#2. An angry constuction worker throws his wench downward from a height of 128 feet with am initial velocity of 32 feet per second. The height of he wrench above the ground after t seconds is given by S(t0 = 16^2-32t+ 128.
A. what is the height of the wrench after 1 second?
.
Plug in the given values into the provided equation of:
S(t) = 16^2-32t+ 128
S(1) = 16^2-32(1)+ 128
S(1) = 256 -32 + 128
S(1) = 224 + 128
S(1) = 352 feet
.
.
B. How long does it take for the wrench to reach the ground?
Set equation to zero and solve for t:
S(t) = 16^2-32t+ 128
0 = 16^2-32t+ 128
0 = 256 -32t+ 128
0 = 384 -32t
32t = 384
t = 12 seconds

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