construct an equilateral triangle ABC in which altitude drawn from opposite vertex is 3.5 cm.Also construct a triangle APR similar to a triangle such that each side of the triangle APR is 1.5 times that of the corresponding side of triangle ABC.
tanA = h/(b/2).
tanA = 3.5 / (b/2).
tan60 = 3.5 / (b/2).
(b/2)tan60 = 3.5.
b/2 = 3.5 / tan60. = 2.02.
b = 4.04 cm.
a = b = c = 4.04 cm.
A = B = C = 60 Deg.
To construct an equilateral triangle ABC with an altitude of 3.5 cm, follow these steps:
1. Draw a line segment AB of any desired length. This will be one side of the equilateral triangle.
2. Set your compass to a radius of 3.5 cm and place the compass point at point A. Draw an arc intersecting the line AB, and label this intersection point as C.
3. Without changing the compass radius, place the compass point at point C and draw another arc to intersect the first arc you drew. Label this intersection point as B.
4. Connect points B and C with a straight line segment.
This will give you an equilateral triangle ABC with an altitude of 3.5 cm.
To construct a triangle APR that is similar to triangle ABC with each side 1.5 times longer, follow these steps:
1. Extend line segment AB beyond point B by 1.5 times its length. Label this extension point as P.
2. Draw a line segment from point P perpendicular to line segment AB, intersecting line segment BC (extended if needed) at point R.
3. Connect points A and R with a straight line segment.
This will give you a triangle APR that is similar to triangle ABC, with each side 1.5 times longer.
To construct an equilateral triangle ABC, follow these steps:
1. Draw a line segment AB of any desired length. This will be one side of the equilateral triangle.
2. From point A, use a compass to draw an arc with a radius equal to the length of AB. This arc should intersect the line segment AB at point C.
3. From point B, use the compass again to draw an arc with the same radius as before. This arc should intersect the previous arc drawn at point C. This point will be the third vertex of the equilateral triangle.
4. Connect points A and C, as well as points B and C, to complete the equilateral triangle ABC.
To construct a triangle APR similar to triangle ABC, such that each side of APR is 1.5 times that of the corresponding side of ABC, follow these steps:
1. Extend side AB of the equilateral triangle ABC beyond point B.
2. With a compass, set the width to 1.5 times the length of AB, and draw an arc from point A that intersects the extension of AB at a point we call P.
3. From point P, draw a line segment parallel to side AC of the equilateral triangle to intersect side BC at a point we call R.
4. Connect points A and R, as well as points P and R, to complete the triangle APR.
Now you have constructed the equilateral triangle ABC and the similar triangle APR.