What is the maximum area of a right triangle with a hypotenuse of 5?

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What is the maximum area of a right triangle with a hypotenuse of 5?

Its area = 3*4/2 = 6 sq cm. An isosceles RAT with its hypotenuse = 5 cm will have the other two sides equal to 5 cos 45. And its area will be [5 cos 45}^2/2 = 6.25 sq cm. So the maximum area of a RAT = 6.25 sq cm.

What is the largest possible area for a right triangle whose hypotenuse is 5 cm long what are its dimensions?

x = 5 2 is the only critical point that makes sens physically, to be a length in a right triangle with hypotenuse 5. Therefore, the other side is y=√25−252=5√2, so, the maximum area is A=254 cm2 and corresponds to the isosceles right triangle with sides 5√2 cm.

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How do you find the maximum area of a right angled triangle?

  1. If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, then the area of the triangle is a maximum when the angle between these sides is θ.
  2. The sum of lengths of the hypotenuse and a side of a right angled triangle is given.

What is the largest possible area for a right triangle in which the sum of the lengths of the two shorter sides is 100 in?

What is the largest possible area for a right triangle in which the sum of the lengths of the two shorter sides is 100 in.? Answer on the back of the book is 1250 in.

Do right triangles have the largest area?

A right angles triangle with a fixed size hypotenuse will have a maximum area if and when both sides are equal – i.e. 2(X squared)=144 which gives you X – as each side of the triangle 8.4853. A right angles triangle is really half of a quadrangle (be it a square or an oblong).

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How do you find the maximum area of a triangle with the perimeter?

For any given perimeter, of all triangles, an equilateral triangle encloses the maximum area. Here, the perimeter is given as, 2s = 100. So s = 50. The area of the equilateral triangle with s = 50 is given by (s^2/4)*3^0.5 =(50^2/4)*3^0.5 = 1082.531755 sq units.

Which triangle has maximum 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.

What value of theta will maximize the triangles area?

Given that the two sides of a triangle have lengths a and b and the angle between them is θ. Thus θ = π/2 will give maximum area.

What is the largest area of the triangle?

The area of a triangle is maximum when one of the three angles is 90° because then the height is maximum, otherwise it is maximum when all the three sides are equal or the triangle is equilateral triangle. Area of a triangle is maximum for a given perimeter when it is a equilateral (nature loves symmetry).

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Which figure has the maximum area?

The circle has the largest area of any two-dimensional object having the same perimeter. A cyclic polygon (one inscribed in a circle) has the largest area of any polygon with a given number of sides of the same lengths.