Sage-Tips

What is the maximum area of an isosceles triangle?

Let the height of the triangle be h . So. A is the geometric mean of two positive quantities : h2 and 9−h2 , which have a given arithmetic mean (namely 4.5). Since the geometric mean of two positive quantities is never larger than their arithmetic mean, the largest possible value for the area is 4.5.

What is the largest area of an isosceles triangle?

Area of isosceles triangle = × l × l × sin θ where, θ is vertex angle of the isosceles triangle. The area is given by × 3×3×sinθ where θ is the vertex angle of the isosceles triangle. Hence, option (4) is correct.

How do you find the uneven side of an isosceles triangle?

To find an unknown side of a triangle, you must know the length of other two sides and/or the altitude. To find the unknown base of an isosceles triangle, using the following formula: 2 * sqrt(L^2 – A^2), where L is the length of the other two legs and A is the altitude of the triangle.

What is the maximum area of an isosceles triangle inscribed in a circle?

The area of the largest isosceles triangle that can be inscribed in a circle of radius 6 is 46.76 square units.

What type of triangle has the largest area?

equilateral one
Among all triangles inscribed in a given circle, the equilateral one has the largest area. Among all triangles inscribed in a given circle, the equilateral one has the largest area.

How to find the perimeter of an isosceles right triangle?

The perimeter of an isosceles right triangle is the sum of all the sides of an isosceles right triangle. Suppose the two equal sides are a. Using Pythagoras theorem the unequal side is found to be a√2. Question 1: Find the area of an isosceles triangle given b = 12 cm and h = 17 cm?

What are the characteristics of an isosceles triangle?

An isosceles triangle has two equal side lengths and two equal angles, the corners at which these sides meet the third side is symmetrical in shape. If a perpendicular line is drawn from the point of intersection of two equal sides to the base of the unequal side, then two right-angle triangles are generated.

How do you find the altitude of an isosceles triangle?

If the length of the equal sides and the length of the base of an isosceles triangle are known, then the height or altitude of the triangle is to be calculated using the following formula: The Altitude of an Isosceles Triangle = √ (a2 − b2/4)

How to find the sides of an equilateral triangle?

The sides of an equilateral triangle are 9.4 cm, correct to the nearest one decimal place. Work out the upper bound of the side of this triangle. The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p. Draw angle |∠ ABC| = 130° and built its axis.