RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.

Correct answer:

c =  13 cm
a =  12 cm
b =  5 cm

Step-by-step explanation:

$$\begin{gathered} a+b=17\text{ cm } \\ r=2\text{ cm } \\ r={\displaystyle \frac{a+b-c}{2}} \\ a+b=c+2r \\ c=17-2\cdot r=17-2\cdot 2=13\text{ cm} \end{gathered}$$

$$\begin{gathered} a^2+b^2=c^2 \\ {a}^2+(17-a{)}^2=13^2 \\ 2a^2-34a+120=0 \\ p=2;q=-34;r=120 \\ D=q^2-4pr=34^2-4\cdot 2\cdot 120=196 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{34\pm \sqrt{196}}{4}} \\ {a}_{1,2}={\displaystyle \frac{34\pm 14}{4}} \\ {a}_{1,2}=8.5\pm 3.5 \\ {a}_1=12 \\ {a}_2=5 \\ \text{ Factored form of the equation: } \\ 2(a-12)(a-5)=0 \\ a=a_1=12\text{ cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=17-a=17-12=5\text{ cm}$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• 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.
• 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.
• Perimeter of RT
  Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm².
• 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.
• 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.
• Rhombus and inscribed circle
  It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
• 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.
• Ratio of sides
  Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• Arc-sector
  arc length = 17 cm area of sector = 55 cm² arc angle = ? the radius of the sector = ?
• 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.
• Medians in right triangle
  It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
• Two chords
  In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle.
• RT - inscribed circle
  In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
• Inscribed circle
  XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
• Medians in RT
  The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
• Triangle
  Calculate the triangle sides if its area S = 630 and the second cathetus is shorter by 17.
• Tangents
  To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.