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neonofarm [45]
3 years ago
5

In ∆ABC, point D is the centroid. If (AE) ̅=15, (BF) ̅=27, and (CD) ̅=8, find the following lengths

Mathematics
1 answer:
Anna71 [15]3 years ago
7 0

Answer:

5,18,12 cms are the answer.

Step-by-step explanation:

Given is a triangle ABC.  Point D is the centroid.  

E,F and G are midpoints of CB, BA and AC respectively.

AE, BF and CG are medians of the triangle.

We know that centroid divides the median in the ratio 2:1

Using this we find that AD:DE = 2:1

Or AD+DE:DE = (2+1):1

AE:DE =3:1

15:DE = 3:1 . Hence DE =5 cm.

On the similar grounds we find that DF = 1/3 BF = 9

Hence BD = DF-BF = 27-9 =18 cm

and also

CG = 3/2 times CD = 12 cm.

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The object on the right is made from a square-based pyramid joined to a cuboid.
spayn [35]

Answer:

Density of steel = 80.73 gm/cm^3

Step-by-step explanation:

The figure is made up of cuboid and square pyramid.

Height of cuboid, h = 9 cm

Length of cuboid, l = 6 cm

Width of cuboid, w = 6 cm

Volume of cuboid is given by the formula:

V_{Cuboid} = l \times w \times h

V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3

Density of Wood , D_{Cuboid}= 0.68g/cm^3

We know that formula of Density is:

Density = \dfrac{Weight}{Volume}

D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}

Putting the values:

W_{Cuboid} = 324 \times 0.68 = 220.32\ gm

Total weight = W_{Cuboid} + W_{Pyramid}

970 = 220.32 + W_{Pyramid}

W_{Pyramid} = 749.68 gm

Volume of pyramid is given as:

V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}

Base is a square with side 6 cm

V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3

Density of Steel/Pyramid:

D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3

5 0
3 years ago
A merchant bought some shirts for $120. The next day the price charged for each shirt was reduced by $1. The merchant calculated
Goshia [24]

Answer:

The merchant buys 30 shirts originally.

Step-by-step explanation:

Let us assume that the merchant bought x numbers of shirts in $120.

So, the cost for each shirt is $\frac{120}{x}.

Now, if the cost for each shirt is reduced by 1$, then he would have bought 10 shirts more i.e. (x + 10) shirts in $120.

So, we can write the following equation as  

(\frac{120}{x} - 1)(x + 10) = 120

⇒(120 - x)(x + 10) = 120x

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⇒ x² +10x - 1200 = 0

⇒ x² + 40x - 30x - 1200 = 0

⇒(x + 40)(x - 30) = 0

⇒ x = - 40 or x = 30

But x can not be negative.

Hence, the merchant buys 30 shirts originally. (Answer)

6 0
3 years ago
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