Sides ratio

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

Correct answer:

o =  48 cm

Step-by-step explanation:

$$\begin{gathered} a_1=10 \\ {b}_1=17 \\ {c}_1=21 \\ S=84 \\ {s}_1=(a_1+b_1+c_1)\mathrm{/}2=(10+17+21)\mathrm{/}2=24 \\ {S}_1=\sqrt{s_1\cdot (s_1-a_1)\cdot (s_1-b_1)\cdot (s_1-c_1)}=\sqrt{24\cdot (24-10)\cdot (24-17)\cdot (24-21)}=84 \\ k=\sqrt{S\mathrm{/}{S}_1}=\sqrt{84\mathrm{/}84}=1 \\ a=k\cdot a_1=1\cdot 10=10 \\ b=k\cdot b_1=1\cdot 17=17 \\ c=k\cdot c_1=1\cdot 21=21 \\ o=a+b+c=10+17+21=48\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• Similar triangles
  Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C' if its circumference is 80 cm?
• Sides od triangle
  Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
• The sides
  The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals
• Similar triangles
  The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm
• Rectangular triangles
  The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8
• Ratio of sides
  Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• Heron backlaw
  Calculate missing side in a triangle with sides 17 and 34 and area 275.
• Ratio of sides
  The triangle has a circumference of 21 cm, and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
• Rectangle 3-4-5
  The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
• Diamond
  Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
• Sss triangle
  Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
• Right triangle - ratio
  The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
• Similarity coefficient
  In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.
• ISO triangle
  Calculate the area of an isosceles triangle KLM if its sides' length is in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
• Circle described
  The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
• Two similar
  Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, 18 cm longer than the first. Find the lengths of its sides.
• Similar triangles
  In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.