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.

Correct answer:

a =  5.547 cm
b =  8.3205 cm

Step-by-step explanation:

$$\begin{gathered} a:b=2:3 \\ b=3\mathrm{/}2\cdot a \\ c=10\text{ cm } \\ {c}^2=a^2+b^2 \\ {c}^2=a^2+(3\mathrm{/}2a{)}^2 \\ {c}^2=a^2+(3\mathrm{/}2{)}^2\cdot a^2 \\ a=\sqrt{{\displaystyle \frac{c^2}{1+(3\mathrm{/}2{)}^2}}}=\sqrt{{\displaystyle \frac{10^2}{1+(3\mathrm{/}2{)}^2}}}=5.547\text{ cm} \end{gathered}$$

$b=3\mathrm{/}2\cdot a=3\mathrm{/}2\cdot 5.547=8.3205\text{ cm}$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• Right triangle
  Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
• RT and ratio
  A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
• Right angled triangle
  The hypotenuse of a right triangle is 17 cm long. When we decrease the length of legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs.
• Isosceles trapezoid
  Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
• 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.
• Cuboid face diagonals
  The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
• Median in right triangle
  In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
• Euclid theorems
  Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
• Sides ratio
  Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21
• Ratio-cuboid
  The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
• RT sides
  Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
• Center of gravity
  In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
• Ratio of edges
  The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
• Right Δ
  A right triangle has the length of one leg 11 cm and the hypotenuse 61 cm size. Calculate the height of the triangle.
• A rectangle 2
  A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
• Rhombus and diagonals
  The a rhombus area is 150 cm² and the ratio of the diagonals is 3:4. Calculate the length of its height.
• 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.