9514 1404 393
Answer:
c.) 57 cm
Step-by-step explanation:
The centroid divides the median into parts with a 2:1 ratio.
OM : OP = 2 : 1
OM : MP = 2 : (2+1) = 2 : 3
As a fraction with MP on top, this is ...
MP/OM = 3/2
MP = (3/2)OM = 3/2×(38 cm)
MP = 57 cm
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<em>Comment on the answer choices</em>
Often, you can eliminate a number of the choices in a multiple-choice question just by testing whether they are reasonable. Here, the longer part of a line segment has length 38, so the whole segment will not be shorter than that. The choices 19 and 25.5 make no sense.
The remaining choices are 114 cm and 57 cm. The former is 3 times the length of the given segment, which the drawing tells us is unreasonable.
The only reasonable choice offered is 57 cm.
IT IS C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC it is c
So with this, I will be using the substitution method. With the first equation, substitute (y+3) into the x variable and solve for y:
Next, now that we have the value of y, substitute it into either equation to solve for x:
<u>And this is how you get your final answer (5,2).</u>
If by "long leg lengths" you mean the hypotenuse then the area is 116 sq. units. If you mean the bases of the triangles then the area is 170 sq. units.
If the length of 12 is the hypotenuse, we first must find the base of the triangles using the Pythagorean theorem:
10² + b² = 12²
100 + b² = 144
b² = 44
b = √44 = 6.6
This means we have two triangles and a rectangle. The area of the rectangle is 5(10) = 50 sq. units. The area of each triangle is 1/2(6.6)(10) = 33. Adding all 3 together we have:
50+33+33 = 116 sq. units.
If the 12 is the base, then we have the rectangle with the area of 5(10) = 50 and two triangles each with an area of 1/2(12)(10) = 60:
50+60+60 = 170 sq. units.
