Posted by **TY** on Sunday, February 19, 2012 at 8:43pm.

An architect is designing a small A-frame 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

- math/geometry -
**Steve**, Sunday, February 19, 2012 at 9:12pm
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

(4x-9)(x-4) = 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

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