Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.

Correct result:

v =  7 m

Solution:

$$\begin{gathered} a^2=3^2+x^2 \\ {a}^2=5^2+y^2 \\ {a}^2=8^2+(y-x{)}^2 \\ {3}^2+x^2=5^2+y^2 \\ {3}^2+x^2=8^2+(y-x{)}^2 \\ {3}^2+x^2=8^2+y^2-2x_y+x^2 \\ {3}^2=8^2+y^2-2x_y \\ x=(8^2-3^2+y^2)\mathrm{/}(2y) \\ y=11\mathrm{/}\sqrt{3}\doteq 6.3509\text{ m } \\ x=(8^2-3^2+y^2)\mathrm{/}(2y)=(8^2-3^2+6.3509^2)\mathrm{/}(2\cdot 6.3509)\doteq 7.5056\text{ m } \\ a=\sqrt{3^2+x^2}=\sqrt{3^2+7.5056^2}\doteq 8.0829\text{ m } \\ {v}^2=a^2-(a\mathrm{/}2{)}^2 \\ v=\sqrt{a^2-(a\mathrm{/}2{)}^2}=\sqrt{8.0829^2-(8.0829\mathrm{/}2{)}^2}=7\text{ m} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Right angled triangle 2
  LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n
• Isosceles triangle
  In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
• Parallels and one secant
  There are two different parallel lines a, b and a line c that intersect the two parallel lines. Draw a circle that touches all lines at the same time.
• Ladder
  Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
• There
  There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a
• Coordinates
  Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• Circle
  The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
• On line
  On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
• 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.
• Lines
  How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
• Railway embankment
  The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• Parametric form
  Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
• On a line
  On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
• Segment
  Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5].
• Vertices of a right triangle
  Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
• Equilateral triangle
  A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
• Right triangle from axes
  A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?