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Darya [45]
3 years ago
12

What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?

Mathematics
1 answer:
AfilCa [17]3 years ago
4 0

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

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a radio station can broadcasts in all directions to a distance of 60 mi. what is the area in which the station can be heard
zaharov [31]

Answer:

Area = PI * radius ^ 2

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Step-by-step explanation:

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3 years ago
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Is the data set approximately periodic?
wolverine [178]

Answer:

Option: C is the correct answer.

       C. Periodic with period 4 and amplitude of about 15.

Step-by-step explanation:

We are given the table of values as:

Hour             1 -- 2 -- 3 --  4 --  5 -- 6 -- 7 -- 8 -- 9 -- 10 -- 11

Number       24-41-10-32-26-38-9-31-25-39-12

of boats

As we could see that after every 4 value the values are approximately repeating.

Hence,the data set is approximately periodic.

Also, the amplitude is calculated as:

Average of the maximum and minimum value of each set

We divide the set into 3 sets as follows:

 Hour                       1           2           3            4

Number of boat      24        41          10           32

Here we have amplitude as:

         (41-10)/2=15.5

 Hour                       5           6           7            8

Number of boat      26        38           9           31

  Amplitude is:

          (38-9)/2=14.5

Hour                       9           10          11            12

Number of boat      25        39          12      

            Amplitude is:

            (39-12)/2=13.5

Hence, we see that the amplitude is about 15.

   

4 0
3 years ago
Points (1,3), (-4,7), and (-29,K) are collinear. Find K.<br><br> How do i solve this?
oee [108]
Co linear points have same slope
<span>Points (1,3), (-4,7), and (-29,K)
m1,2=7-3/-4-1=-4/5

m2,3=K-7/-29+4
m2,3=K-7/-25

-4/5=K-7/-25
4/5=K-7/25
4=K-7/5
20=K-7
K=27
 </span>
3 0
3 years ago
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