Please help with my algebra homework

i have two questions...
1) an object that is projected straight downward with initial velocity v feet per second travels a distance s=vt+16t^2, where t= time in seconds, if ron is standing on a balcony 84 ft above the ground and throws a penny straight down with an initial velocity of 10 ft per second, in how many seconds will it reach the ground?

A) 2 seconds
B) 3 seconds
C) 6 seconds
D) 8 seconds


2) a rectangle has a diagonal that measures 10 cm and a length that is 2 cm longer than the width. what is the width of the rectangle in cm?

A) 5
B) 6
C) 8
D) 12

thank you so much, if you can please explain it to me about the steps

1) = A) 2 seconds
s=vt+16t^2
84=10t+16t^2
subt 84 both sides
0=16t^2+10t-84
factor
0=2(8t^2+5t-42)
factor bracket using quadratic eqn
a=8, b=5, c=-42
t= (-(5) +- sq rt ( (-5)^2-4 (8) (-42) )/2(8)
t=(-5+- sq rt ( 25 + 1344) )/16
t= (-5 +- sq rt (1369) 0/16
t= (-5 +- 37)/16
t= (-5-37)/16=-2.625 not realistic, neg time
or t= (-5+37)/16= +2 seconds
checking
s=vt+16t^2
84=10(2) +16(2^2)=20+62=84

2) = B) 6
a^2+b^2=c^2
a^2+(a+2)^2=10^2
a^2+a^2+4a+4=100
2a^2+4a+4-100=0
2a^2+4a-96=0
2(a^2+2a-48)=0

2(a+8)(a-6)=0
a-6=0
a=6 cm. ans. for the short side.
6+2=8 cm. ans. for the long side.
Proof:
6^2+8^2=100
36+64=100
100=100

So the width is 6cm, and the length is x+2=8 cm