In ΔABC, centroid D is on median AM. AD = x + 3 and DM = 2x - 1. Find AM.

Mathematics

2 answers:

nata0808 [166]4 years ago

3 0

check the picture below

DochEvi [55]4 years ago

3 0

Answer:

Option A

Step-by-step explanation:

Given that in triangle ABC AM is one median

D is the centroid

We know by triangle conjectures that

in any triangle centroid divides median in the ratio 2:1

i.e. If D is centroid on AM,

then AD:DM =2:1

Substitute for AD and DM the given values

$x+3:2x-1 =2:1\\x+3 =2(2x-1)\\x+3=4x-2\\5=3x\\Or x=\frac{5}{3}$

Hence answer is the length of AM

= AD+DM

= $x+3+2x-1\\=3x+2\\=3(\frac{5}{3} )+2\\=7$

Option A is the answer

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Work Shown:

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Explanations:

There are quite a bit of steps. I decided to break things into two parts.
The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
Afterward, I gave each fraction the LCD mn. I multiplied top and bottom of the first fraction by n/n. I did a similar operation to the second fraction, but with m instead.
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