# Sides ratio

Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21

Result

o =  48 cm

#### Solution:

$a_{ 1 } = 10 \ \\ b_{ 1 } = 17 \ \\ c_{ 1 } = 21 \ \\ \ \\ S = 84 \ \\ \ \\ s_{ 1 } = (a_{ 1 }+b_{ 1 }+c_{ 1 })/2 = (10+17+21)/2 = 24 \ \\ S_{ 1 } = \sqrt{ s_{ 1 } \cdot \ (s_{ 1 }-a_{ 1 }) \cdot \ (s_{ 1 }-b_{ 1 }) \cdot \ (s_{ 1 }-c_{ 1 }) } = \sqrt{ 24 \cdot \ (24-10) \cdot \ (24-17) \cdot \ (24-21) } = 84 \ \\ k = \sqrt{ S/S_{ 1 } } = \sqrt{ 84/84 } = 1 \ \\ a = k \cdot \ a_{ 1 } = 1 \cdot \ 10 = 10 \ \\ b = k \cdot \ b_{ 1 } = 1 \cdot \ 17 = 17 \ \\ c = k \cdot \ c_{ 1 } = 1 \cdot \ 21 = 21 \ \\ o = a+b+c = 10+17+21 = 48 = 48 \ \text{ cm }$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Check out our ratio calculator.

## Next similar math problems:

1. Triangle perimeter
Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
2. Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
3. The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine t
4. Median
The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
7. Numbers at ratio
The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?
8. Donuts
Find how many donuts each student will receive if you share 126 donuts in a ratio of 1:5:8
9. Sines
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
10. Triangle
Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
11. Center traverse
It is true that the middle traverse bisects the triangle?
12. Liters od milk
The cylinder-shaped container contains 80 liters of milk. Milk level is 45 cm. How much milk will in the container, if level raise to height 72 cm?
13. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
14. Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
15. Mean
A student food the mean of 50 items as 38.6. When checking the work he found that he had taken one item as 50 why it should correctly read as 40 in this circumstances. What should be the correct mean?
16. One half
One half of ? is: ?
17. Coefficient
Determine the coefficient of this sequence: 7.2; 2.4; 0.8