math/geometry
posted by TY on .
An architect is designing a small Aframe cottage for a new resort area. A cross section of the cottage is an isosceles triangle with an area of 98 square feet. The front wall of the cottage must a accommodate a sliding door that is 6 feet wide and 8 feet high. Find the width and height of the cross section

center the door way so that half the base is 3+x feet. The area of the triangle is 98, so the height h = 98/(3+x)
using similar triangles,
8/x = h/(x+3)
8(x+3) = hx
8(x+3) = 98/(x+3) * x
4x^2  25x + 36 = 0
(4x9)(x4) = 0
Looks like any x from 9/4 to 4 will work. So, the dimensions can vary from
10.5 ft wide x 18 2/3 ft high
to
14 wide x 16 ft high 
Puzsy