RT sides

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

Correct result:

c =  13 cm
a =  12 cm
b =  5 cm

Solution:

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

$$\begin{gathered} a^2+b^2=c^2 \\ {a}^2+(17-a{)}^2=13^2 \\ 12^2+(17-12{)}^2=13^2 \\ a=a_1=12=12\text{ cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

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

Try calculation via our triangle calculator.

Try another example

Showing 0 comments:

Next similar math problems:

• Euclid theorems
  Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
• A bridge
  A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
• Sides of right angled triangle
  One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
• Diagonal 20
  Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
• Ratio of sides
  Calculate the area of a circle that has 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.
• 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.
• Isosceles triangle 9
  Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
• 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?
• Circle and square
  An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
• Perimeter and legs
  Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm².
• 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.
• MO SK/CZ Z9–I–3
  John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
• Two chords
  Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
• 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.
• 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.
• Faces diagonals
  If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
• An equilateral
  An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?