Isosceles triangle

The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.

Correct answer:

S =  588 cm2

Step-by-step explanation:

o=112 cm a:b=6:5 o=a+2b 6a/5=b o=a+2 5a/6 a=o/(1+2 5/6)=112/(1+2 5/6)=42 cm b=5 a/6=5 42/6=35 cm o1=a+2 b=42+2 35=112 cm h=b2(a/2)2=352(42/2)2=28 cm S=a h/2=42 28/2=588 cm2

Try calculation via our triangle calculator.




Did you find an error or inaccuracy? Feel free to write us. Thank you!



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 a quadratic equation?
See also our right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Isosceles triangle
    iso_tr In an isosceles triangle, the arm's length and the length of the base are in ratio 3 to 5. What is the length of the arm?
  • Isosceles trapezoid
    lichobeznik Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  • Arm and base
    rr_triangle3 The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
  • Arm-leg
    triangles2 Calculate the length of the base of an isosceles triangle with a circumference 224 cm if the arm length is 68 cm.
  • A isosceles
    rr_triangle3 A isosceles triangle has an area of 168 cm2 and it's added height and base is 370 cm. What are the measurements of it's height and base?
  • Base of an isosceles triangle
    rr_triangle3 Calculate the size of the base of an isosceles triangle, the height is 5 cm and the length of the arm is 6.5 cm. What is the perimeter of this triangle?
  • ISO triangle
    rr Calculate the area of an isosceles triangle KLM if its sides' length is in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
  • Ratio of sides
    trojuholnik The triangle has a circumference of 21 cm, and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
  • Isosceles triangle 9
    iso_triangle Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.
  • Isosceles trapezoid
    rr_lichobeznik Find the area of an isosceles trapezoid, if the bases are 12 cm and 20 cm, the length of the arm is 16 cm
  • Rectangle
    obdlznik The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
  • Triangles
    green_triangle Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle.
  • The circumference
    rectangle The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
  • Right triangle
    righttriangle 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.
  • Right triangle eq2
    rt_triangle Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  • Isosceles triangle
    triangles Calculate the area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
  • Isosceles trapezoid
    rr_lichobeznik Find the height in an isosceles trapezoid if the area is 520 cm2 and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid.