*See attachment for the simplified model of the monument
Answer:
The correct option is B. 13ft.
YES to option B. NO to A and C.
Step-by-step Explanation:
=>Given: Model of the monument consisting of a rectangular pyramid and a rectangular prism having a total volume of 66ft³.
Volume of monument = Volume of Pyramid + Volume of Prism = 66ft³
=>Dimensions of given rectangular pyramid:
base length (l) = 3ft
base width = 2ft
height of pyramid (h) = ? (h = Unknown)
Base Area (B) = l × w = 3 × 2 = 6ft²
Volume of pyramid = ⅓ × base area (B) × h = ⅓ × 6 × h
V of Pyramid = 2h ft³
=> Dimensions of the rectangular prism:
base length (l) = 3ft
base width (w) = 2ft
Height of prism (h) = 10ft
Base area (B) = l × w = 3 × 2 = 6 ft³
Volume of prism = base area (B) × height (h)
V of prism = 6 × 10 = 60 ft³
We are required to find the possible height of the monument.
Height of monument = height of pyramid + height of prism
Height of pyramid is unknown (h)
Height of prism = 10ft
Let's find the height of the pyramid using the Volume of the monument = volume of pyramid + volume of prism
Thus,
V of monument = 66 ft³
V of pyramid = 2h ft³
V of prism = 60 ft³
Therefore,
66 = 2h + 60
Subtract 60 from both sides
66 - 60 = 2h + 60 - 60
6 = 2h
Divide both sides by 2
3 = h
Height of pyramid (h) = 3ft
Height of monument = h of Pyramid + h of prism
Height of monument = 3 + 10
Height of monument = 13ft.
The correct option is B. 13ft.
YES to option B. NO to A and C.
Answer:
option B. MB/AM=NC/AN
Step-by-step explanation:
we know that
The <u><em>Triangle Proportionality Theorem</em></u> states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally
In this problem
MN is parallel to BC
MN intersect AC and divide into AN and NC
MN intersect AB and divide into AM and MB
so
Applying the Triangle Proportionality Theorem
Rewrite