Only option 1 and 4 are true.
Points S, U, and T are the midpoints of the sides of ΔPQR.
ΔSUT is inside of ΔPQR. Points S, U, and T are the midpoints of ΔPQR.
Which statements are correct? Check all that apply.
1. QP = UT
2. One-halfTS = RQ
3. SU = PR
4. SU ∥ RP
5. UT ⊥ RP
Given to us,
S, U, and T are the midpoints of the sides of ΔPQR.
Using Triangle Midpoint Theorem, which states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Therefore, only option 1 and 4 are true.
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Answer:
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Step-by-step explanation:
Answer:
Base of each triangular face = 4 inches
Height of each triangular face = 6 inches
Step-by-step explanation:
The length of each side of the square base is the base of each isosceles triangle forming the pyramid.
We know from our problem that the ratio of the height of each triangle to its base is 3:2, so . We also know that the base is a square with sides 4 inches long, since the bade of the square is the base of the isosceles triangle, .
Replacing the value of the base in our proportion:
Multiply both sides by 4
We can conclude that he base of each isosceles triangle is 4 inches and its height is 6 inches.
The perimeter in this case is:
y + 2x = 5000
The area is:
A = x * y
We rewrite the area:
A = x * (5000-2x)
A = 5000x-2x ^ 2
We derive:
A '= 5000-4x
We equal zero and clear x:
0 = 5000-4x
4x = 5000
x = 5000/4
x = 1250
We look for the other dimension:
y = 5000-2x
y = 5000-2 (1250)
y = 5000-2500
y = 2500
Then, the area will be:
A = (2500) * (1250)
A = 3125000 m ^ 2
Answer:
The largest area that can be enclosed is:
A = 3125000 m ^ 2
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