1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svlad2 [7]
3 years ago
8

What is the sum of the squares of the lengths of the $\textbf{medians}$ of a triangle whose side lengths are $10,$ $10,$ and $12

$?

Mathematics
2 answers:
Arturiano [62]3 years ago
7 0

Answer:

258.

Step-by-step explanation:

We have been given measure of sides of a triangle. We are asked to find sum of the squares of the lengths of the medians of a triangle.    

We will use Apollonius's theorem to solve our given problem. This theorem states that 3 times the sum of squares of the sides of a triangle is equal to 4 times the sum of squares of the medians of the triangle.

Using Apollonius's theorem, we can set an equation as:

3(10^2+10^2+12^2)=4(\text{Sum of squares of the length of medians})

4(\text{Sum of squares of the length of medians})=3(10^2+10^2+12^2)

4(\text{Sum of squares of the length of medians})=3(100+100+144)

4(\text{Sum of squares of the length of medians})=3(344)

\frac{4(\text{Sum of squares of the length of medians})}{4}=\frac{3(344)}{4}

\text{Sum of squares of the length of medians}=3*86

\text{Sum of squares of the length of medians}=258

Therefore, the sum of squares of the length of medians of the given triangle is 258.

FrozenT [24]3 years ago
4 0

A picture can help.

The median to the long side divides the isosceles triangle into two right triangles with hypotenuse 10 and short leg 6. Thus the long leg (median of interest) is found by the Pythagorean theorem to be

... √(10² -6²) = √64 = 8

Then the midpoint of the short side is found to be 6 + (6/2) = 9 units to the side and 8/2 = 4 units above the opposite vertex. Hence the square of the length of that median is 9² + 4² = 97.

The sum of squares of interest is

... 8² + 2×97 = 258

You might be interested in
Winnie poured 14 cups of water into a rectangular container measuring 13 inches by 7 inches by 6 centimeters. [1 cup = 14.44 cub
Alex_Xolod [135]
Part A: 
<span>Max volume = Volume of container = 13 in x 7 in x 6 in = 546 in^3 </span>

<span>Part B: </span>
<span>1 cup = 14.4375 in^3 </span>
<span>
14 cups = 14.4375 in^3 x 7 = 202.125 in^3 </span>

<span>Part C: </span>
<span>Height of water = (202.125 in^3)/(13 in x 7 in) = 2.22 in.</span>
8 0
3 years ago
A tap running 20ml a minute. How long to a fill a litre. In minutes please
zhannawk [14.2K]

Answer:

20ml in 1 minute. 1000ml is equal to 1 litre.

Step-by-step explanation:

1000/20 = 50

. 50 minutes will take to fill a litre

6 0
2 years ago
Read 2 more answers
The volume of cube is 343 cubic centimeters.What is the suface area of the cube
Ann [662]
The cube root of 343 is 7.
One side has an area of 7*7 = 49 square cm
There are 6 sides to a cube
6 * 49 is the surface area = 294
7 0
3 years ago
Jeff uses the expression 2(3b + 1) to determine how many books (b) he needs to order for his store. If b = 12, how many books sh
kari74 [83]

Answer:

73

Step-by-step explanation:

you write 12 instead of b

4 0
3 years ago
Read 2 more answers
Find the two numbers whose deference is 10 and sum is 34​
mezya [45]

Answer:

the correct answer is 22 and 12

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Other questions:
  • 5.
    10·1 answer
  • Which equations are true?
    10·1 answer
  • Which pairs of points would result in a line with a rate of change of 2:1? select all that apply
    9·1 answer
  • Whats the answer to this problem????<br><br><br>the product of 6 and a number p is 24
    14·1 answer
  • Convert 0.000002954 to scientific notation
    7·2 answers
  • Consider the sequence 1, –3, 9, –27, 81, … Which statement describes the sequence?
    5·2 answers
  • Y-x=160<br> Help plz pleaseeeee
    12·1 answer
  • Aplica el método de eliminación Gaussiana
    7·1 answer
  • Steve studies math for 7/8 of an hour and history for 2/3 of an hour. How many hours did he study?
    15·1 answer
  • Question 8 of 10<br> Simplify (7 + 1)2 – (11 + 32) - 4.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!