what is the area of a golden triangle whose height is 7?

Answer 1

A "golden triangle" employs the "golden ratio" in its construction. The golden ratio is (1+√5)/2. A golden triangle is an isosceles triangle in which the ratio of one of the two equal sides to the base is (1+√5)/2.

The area of a triangle is .5*h*B, where h = altitude, and B is the base. In an isosceles triiangle, the h^2 = L^2 - (B/2)^2. (The altitude divides the triangle into two right triangles of hypotenuse L and base B/2.) As said above, the ratio L/B = (1+√5)/2, so L = B*(1+√5)/2. Now we have the relation (using this latter equ for L):

h^2 = [B*(1+√5)/2]^2 - (B/2)^2 Solve for B:

B^2 = h^2/{(1+√5)/2]^2 - .5^2}

B = h/√[(1+√5)/2]^2 - .5^2]

You have h, solve for B, and compute .5*h*B

Answer 2

What is the width of the triangle?