find the maximum area of a triangle if has a perimeter equal to 18.........
2007-08-18 00:30:37 · 5 answers · asked by rhez 1 in Science & Mathematics ➔ Mathematics
For a triangle to have the maximum area for a given perimeter, it must be an equilateral triangle. Each side (a) = 18/3 = 6 units.
Area of an equilateral triangle = a^2 * sqrt(3)/4
= 6^2 * sqrt(3)/4
= 9*sqrt(3) square units
= 15.588 sq. units (approx.)
2007-08-18 00:36:57 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
The maximum area is obtained by having equal sides, so each side must be 6 units.
Using Pythagoras' gives the height as
sqrt(6^2 - 3^2)
= sqrt(27)
= 3*sqrt(3)
then area
= (1/2)*6*3*sqrt(3)
= 9*sqrt(3)
which is a bit less than 16 sq units.
2007-08-18 07:37:16 · answer #2 · answered by Hy 7 · 0⤊ 0⤋
Max area must be equilateral triangle, ie 6 each side.
Each half triangle is (3 x sqrt27)/2
So area = 3 x sqrt27
2007-08-18 07:38:21 · answer #3 · answered by Anonymous · 0⤊ 0⤋
An equilateral triangle has the most area: 6x6x6 with height 6sin66.6
A = 1/2*6*6sin66.6 = 16.5
2007-08-18 07:35:59 · answer #4 · answered by gebobs 6 · 0⤊ 1⤋
it is about 16units squared
2007-08-18 07:54:21 · answer #5 · answered by Anonymous · 0⤊ 1⤋