# math/geometry

posted by .

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 -

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

• math/geometry -

Puzsy

## Similar Questions

1. ### math

Three men (Tom, peter, and jack)and three women (Eliza, Anne, and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her owm cottage. There are no others staying in …
2. ### math

Three men (Tom, peter, and jack)and three women (Eliza, Anne, and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her owm cottage. There are no others staying in …
3. ### main ideas

what purpose dose question 3-6 serve in the paragragh . Myfamily has a quaint cottage at a small private lake. The cottage is about 75 years old but we try to keep it in good condition

Martin Ellingham is negotiating to buy a vacation cottage in Port Wenn. The seller of the cottage is asking \$186,000. Martin offered him a cash deal, owner-seller (no broker) only if the seller would reduce the price by 12%. The seller …
5. ### math

The director of the center has asked you to design a garden. The director has asked you to design different sections of the garden that meet the following: Section 1 must be shaped like a square. Section 1 must have an area between …
6. ### help (check)

I think its (at a beach cottage) Which words make up the prepositional phrase in this sentence?
7. ### Geometry

Can anybody help me with this word problem?
8. ### FIN 4018 - INCOME TAX PLANNING

Jim acquired a house in 2011 for \$400,000. In 2013, he acquired a cottage for \$150,000. He lived in the house in the winter and in the cottage in the summer. In 2015, he sold both properties. He received \$500,000 for the house and …
9. ### Math geometry

An architect is designing an A-frame cottage for a resort. A cross section of the cottage is an isosceles triangle. The front wall of the cottage must accommodate a sliding door. Knowing that the architect is allowed a rectangular …
10. ### Geometry

Isosceles triangle ABE of area 100 square inches is cut by CD into an isosceles trapezoid and a smaller isosceles triangle. The area of the trapezoid is 75 square inches. If the altitude of triangle ABE from A is 20 inches, what is …

More Similar Questions