Question

1.What is the volume of this rectangular prism?(picture 1)

A) 11 cm3
B) 24 cm3
C) 30 cm3
D) 36 cm3

2.AB = x + 15
AD = 2x + 18
BC = 3 - x
CD = 3x + 25
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 3
B) x = -5
C) x = -11
D) x = 11/2

Answer 1

1.What is the volume of this rectangular prism? (Picture 1)
A) 11 cm3
B) 24 cm3
C) 30 cm3
D) 36 cm3

For this case what you should do is use the following equation:
V = b * h * t
Where
b: base
h: height
t: depth.
Substituting the values:
V = (2) * (6) * (3)
V = 36cm ^ 3
Answer:
the volume of this rectangular prism
D) 36 cm3

2.AB = x + 15
AD = 2x + 18
BC = 3 - x
CD = 3x + 25
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 3
B) x = -5
C) x = -11
D) x = 11/2
The first thing we must do is to see two congruent sides:
Let's evaluate AD = BC
We have:
2x + 18 = 3 - x
We clear x:
2x + x = 3-18
3x = -15
x = -5
Check the value:
AB = DC
x + 15 = 3x + 25
Substituting x:
-5 + 15 = 3 (-5) + 25
10 = -15 + 25
10 = 10
Both sides have the same measure for x = -5.
Answer:
Quadrilateral ABCD is a parallelogram because:
Both sides have the same measure for x = -5.
B) x = -5