RT and ratio

A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?

Correct answer:

a =  30.411 m
b =  60.821 m

Step-by-step explanation:

$$\begin{gathered} c=68m \\ {a}^2+b^2=c^2 \\ a:b=6:12 \\ a=6\mathrm{/}12\cdot b \\ (6\mathrm{/}12{)}^2{b}^2+b^2=c^2 \\ {b}^2(1+(6\mathrm{/}12{)}^2)=c^2 \\ b={\displaystyle \frac{c}{\sqrt{1+(6\mathrm{/}12{)}^2}}} \\ b={\displaystyle \frac{68}{\sqrt{1+(6\mathrm{/}12{)}^2}}}=60.821m \\ a=(6\mathrm{/}12)\cdot b=30.411\text{ m} \end{gathered}$$

$b=68\mathrm{/}\sqrt{1+6\cdot 6\mathrm{/}12\mathrm{/}12}=60.821\text{ m}$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• 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.
• 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.
• Difference of legs
  In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle.
• Trapezoid RT
  The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumpti
• The rope
  A 68-centimeter long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimeters. What is the distance between the other two corners?
• Rhombus 2
  Calculate the rhombus area, which has a height v=48 mm and shorter diagonal u = 60 mm long.
• RT - hypotenuse and altitude
  Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
• 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).
• RT 11
  Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
• 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.
• RT perimeter
  The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
• 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.
• Estate
  An estate-shaped rectangular trapezoid has bases long 34 m, 63 m, and perpendicular arm 37 m. Calculate how long its fence is.
• RT leg and perimeter
  Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
• Rectangular field
  A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
• Tent
  Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
• Cone and the ratio
  The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.