# Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.

Result

a =  21
b =  20
c =  29
A =  46.397 °
B =  43.603 °
C =  90 °

#### Solution:

$S=210 \ \\ o=70 \ \\ \ \\ o=a+b+c \ \\ S=ab/2 \ \\ \ \\ o=a+b+\sqrt{ a^2+b^2 } \ \\ 2S=ab \ \\ \ \\ b=2S/a \ \\ \ \\ 70=a+420/a+\sqrt{ a^2+(420/a)^2 } \ \\ 70a=a^2+420+\sqrt{ a^4+420^2 } \ \\ 70a-a^2-420=\sqrt{ a^4+420^2 } \ \\ a^4 - 140 \ a^3 + 5740 \ a^2 - 58800 \ a + 176400=a^4+420^2 \ \\ - 140 \ a^3 + 5740 \ a^2 - 58800 \ a + 176400=420^2 \ \\ 140 \ a^3 - 5740 \ a^2 + 58800 \ a=0 \ \\ \ \\ \ \\ 140 \ a^2 - 5740 \ a + 58800=0 \ \\ 140a^2 -5740a +58800=0 \ \\ \ \\ p=140; q=-5740; r=58800 \ \\ D=q^2 - 4pr=5740^2 - 4\cdot 140 \cdot 58800=19600 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 5740 \pm \sqrt{ 19600 } }{ 280 } \ \\ a_{1,2}=\dfrac{ 5740 \pm 140 }{ 280 } \ \\ a_{1,2}=20.5 \pm 0.5 \ \\ a_{1}=21 \ \\ a_{2}=20 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 140 (a -21) (a -20)=0 \ \\ \ \\ a=a_{1}=21$

Checkout calculation with our calculator of quadratic equations.

Try calculation via our triangle calculator.

$b=2 \cdot \ S/a=2 \cdot \ 210/21=20 \ \\ b=a_{2}=20$
$c=\sqrt{ a^2+b^2 }=\sqrt{ 21^2+20^2 }=29$
$A=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(a/c)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(21/29) \doteq 46.3972 \doteq 46.397 ^\circ \doteq 46^\circ 23'50"$
$B=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(b/c)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(20/29) \doteq 43.6028 \doteq 43.603 ^\circ \doteq 43^\circ 36'10"$
$C=90=90 ^\circ$

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!

Tips to related online calculators
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?
Pythagorean theorem is the base for the right triangle calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

## Next similar math problems:

1. 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.
2. Right angled triangle
Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
3. RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
4. Catheti
The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
5. Variable
Find variable P: PP plus P x P plus P = 160
6. Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
7. Equation 23
Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
9. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
10. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
11. Discriminant
Determine the discriminant of the equation: ?
12. 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?
13. 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.
14. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
15. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
16. Men, women and children
On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
17. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2