What is the Area of a Triangle Equilateral that's base is 3ft?

What are the dimensions of the triangle (height and base)?

• A triangle has a height 3ft. shorter than 2 times its base.The area is 43.66ft.

• Answer:

  Base = x Height = y Area, A = 43.66 sq. ft. y = 2x + 3 ................... Eq. 1 1/2 xy = A................... Eq. 2 Subbing (2x + 3) from Eq. 1 for y and 43.66 for A in Eq. 2, 1/2 [x(2x + 3)] = 43.66 1/2 (2x² + 3x) = 43.66 2x² + 3x = 2(43.66) 2x² + 3x = 87.32 2(x² + 1.5x) = 87.32 x² + 1.5x = 87.32 / 2 x² + 1.5x = 43.66 x² + 1.5x + 0.5625 = 43.66 + 0.5625 (x + 0.75)² = 44.22 x + 0.75 = √44.22 x + 0.75 = ± 6.65 x = - 0.75 ± 6.65 If x = - 0.75 + 6.65, x = 5.9 If x = - 0.75 - 6.65, x = - 7.5 Feasible Domain: x > 0 Since x = - 7.5 is not in the feasible domain, x = 5.9 and y = 2(5.9) + 3 y = 11.8 + 3 y = 14.8 so Height = 5.9 ft. ¯¯¯¯¯¯¯¯¯¯¯¯ Base = 14.8 ft. ¯¯¯¯¯¯¯¯¯¯¯¯