Question 1:
For this case, the first thing to do is find the side of the square.
We have then that the perimeter is:
P = 4L
Clearing L:
L = P / 4
Substituting values:
L = 48/4
L = 12
We now look for the length of the diagonal.
for this we use the Pythagorean theorem:
d = root ((L) ^ 2 + (L) ^ 2)
d = root ((12) ^ 2 + (12) ^ 2)
d = 16.97 feet
Rounding:
d = 17 feet
Answer:
G option
d = 17 feet
Question 2:
For this case we have the following equation:
2a - 6 + 5a = 3a + 10
We solve the equation. To do this, we clear to.
2a + 5a + 3a = 10 + 6
a * (2 + 5 + 3) = 16
10a = 16
a = 16/10
a = 1.6
Rounding off we have:
a = 2
Answer:
a = 2
Question 3:
For this case the coordinates of the midpoint are:
C = (((x1 + x2) / 2), ((y1 + y2) / 2))
Substituting values:
C = (((-3 + 4) / 2), ((2 + 8) / 2))
Rewriting we have:
C = ((1/2), (10/2))
C = (0.5, 5)
We use the formula of distance between points:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
Then, the distance AC is:
AC = root ((0.5 - (- 3)) ^ 2 + (5-2) ^ 2)
AC = 4.61 units
Answer:
AC = 4.61 units
option A