SOLUTION: A side of a house is in the shape of an isosceles triangle which fits exactly on top of a rectangle. The rectangle is 4 times as long as it is high, and the altitude of the triang

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A side of a house is in the shape of an isosceles triangle which fits exactly on top of a rectangle. The rectangle is 4 times as long as it is high, and the altitude of the triang      Log On


   

Question 965409: A side of a house is in the shape of an isosceles triangle which fits exactly on top of a rectangle. The rectangle is 4 times as long as it is high, and the altitude of the triangular part is 1m less than the height of the rectangle. The total area of the side is 60m^2. Find the height of the house.
Please and thank you!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Picking and analyzing variables was done piece-by-piece but not done in the order shown here:

TRIANGLE
a, altitude
a=-1+h
base of this triangle is L
RECTANGLE
h, height
L, length
L=4h

"Total area of the side", appears to mean, the area of the isosceles triangle, is 60 square meters. Formula for area of triangle should conform to %281%2F2%29a%2AL=60.
%281%2F2%29a%2A4h=60
%281%2F2%29%28h-1%29%284h%29=60
4h%28h-1%29=120
h%28h-1%29=30
h%5E2-h-30=0
%28h%2B5%29%28h-6%29=0
The positive value you want is highlight%28h=6%29.
Now use this value to evaluate the ALTITUDE a, of the isosceles triangle.
-
a=h-1
a=6-1
highlight%28a=5%29