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.

Correct result:

x =  24

Solution:

$$\begin{gathered} S=ab\mathrm{/}2=24 \\ 2\cdot 24=0.75a^2 \\ a=\sqrt{2\cdot 24\mathrm{/}0.75}=8cm \\ b=0.75a=6cm \\ {c}^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}=10cm \\ x=a+b+c=8+6+10=24 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Triangular prism
  The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
• Right triangle eq2
  Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
• Square
  Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm². Determine the side length of the original square.
• Rectangle diagonals
  It is given rectangle with area 24 cm² a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
• Rectangular trapezium
  Calculate the perimeter of a rectangular trapezium when its content area is 576 cm² and sice a (base) is 30 cm, height 24 cm.
• ISO trapezoid v2
  bases of Isosceles trapezoid measured 20 cm and 4 cm and its perimeter is 55 cm. What is the are of a trapezoid?
• 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.
• AP RT triangle
  The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
• Isosceles triangle 9
  Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.
• Rectangle
  The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
• Right angle
  In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
• 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.
• Hypotenuse
  Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
• Right isosceles
  Calculate area of the isosceles right triangle which perimeter is 26 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:
• R Trapezium
  Rectangular trapezium has bases 12 and 5 and area 84 cm². What is its perimeter?
• The right triangle
  The right triangle ABC has a leg a = 36 cm and an area S = 540 cm². Calculate the length of the leg b and the median t2 to side b.