# RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m.
How long are hypotenuse segments?

Result

gb =  36 m
gt =  81 m

#### Solution:

$g_b+g_t=117 \ \\ g_b \cdot g_t = 54^2 \ \\ \ \\ g^2 -117g +2916 =0 \ \\ \ \\ a=1; b=-117; c=2916 \ \\ D = b^2 - 4ac = 117^2 - 4\cdot 1 \cdot 2916 = 2025 \ \\ D>0 \ \\ \ \\ g_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 117 \pm \sqrt{ 2025 } }{ 2 } \ \\ g_{1,2} = \dfrac{ 117 \pm 45 }{ 2 } \ \\ g_{1,2} = 58.5 \pm 22.5 \ \\ g_{1} = 81 \ \\ g_{2} = 36 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (g -81) (g -36) = 0 \ \\ \ \\ g_b=36 \ \text { m }$
$g_t = 81 \ \text { m }$

Try calculation via our triangle calculator.

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!

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

Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? See also our right triangle calculator. See also our trigonometric triangle calculator.

## Next similar math problems:

1. Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
2. Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
3. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
4. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
5. Discriminant
Determine the discriminant of the equation: ?
6. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
7. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
9. Children
The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
10. Three workshops
There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
11. 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?
12. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
13. Stones 3
Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
14. Three unknowns
Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
15. Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
16. Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
17. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15