RT and ratio

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

Result

a =  30.411 m
b =  60.821 m

Solution:

c=68 m a2+b2=c2 a:b=6:12 a=6/12⋅b (6/12)2b2+b2=c2 b2(1+(6/12)2)=c2 b=c1+(6/12)2 b=681+(6/12)2=60.821 m a=(6/12)⋅b=30.411 mc = 68\ m \ \\ a^2+b^2 = c^2 \ \\ a:b = 6:12 \ \\ a = 6/12 \cdot b \ \\ (6/12)^2b^2 + b^2 = c^2 \ \\ b^2(1+(6/12)^2) = c^2 \ \\ b = \dfrac{c}{ \sqrt{ 1+ (6/12)^2}} \ \\ b = \dfrac{ 68 }{ \sqrt{ 1+ (6/12)^2}} = 60.821 \ m \ \\ a = (6/12) \cdot b = 30.411 \ \text{m}
b=68/1+6⋅ 6/12/12=60.821 mb=68 / \sqrt{ 1+6 \cdot \ 6/12/12 }=60.821 \ \text{m}

Try calculation via our triangle calculator.


Try another example


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...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Check out our ratio calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. 1.5 divided
    eq2_3 1.5 divided by 1 = w divided by 4
  2. Unknown number 24
    numbs_6 f we add 20, we get 50% of its triple. What is this unknown number?
  3. Rectangular triangle PQR
    solving-right-triangles In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
  4. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  5. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  6. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  7. Broken tree
    broken_tree The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
  8. Stairway
    schody Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
  9. Ladder
    rebrik_2 The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.
  10. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  11. Windbreak
    vichrica A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
  12. Given
    1998-4b Given 2x =0.125 find the value of x
  13. Unknown number
    nums Identify unknown number which 1/5 is 40 greater than one tenth of that number.
  14. Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  15. Candy
    friends Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have?
  16. Holidays - on pool
    pool_4 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?
  17. Equation
    rovnice_3 Solve the equation: 1/2-2/8 = 1/10; Write the result as a decimal number.