The photo shows a traditional thached house as found in Santana, Madeira in Portugal. The front of the house is in the shape of a triangle. Suppose the base of the triangle is 1 m less than its height and the area of the triangle in 15 m2. Find the height of the triangle. (Hint: Use A= 1/2bh)
Area = 1/2 base * height and A = 15
therefore 15 = (1/2x) * (x + 1)
15 = x^2 / 2 + x/2
30 = x^2 + x
x^2 + x - 30 = 0
(x + 6) (x - 5) = 0 from factorizing
Therefore x = 5 since x cant be a negative number
so base = 5m and height = 6m
-Hayley :)
I assume this house front is an ISOSCELES triangle
The height is listed as (b+1) if you drop a plumbline from the apex (which means you draw a line from the high point to the base) you will create TWO RIGHT triangles with two legs legs that measure h (which is (b+1)) and 1/2b
the area of EACH of these triangles is 1/2 x Leg1 x Leg2 = 1/2 (b+1)(1/2b) but there is TWO of these triangles, so the total area is two times this
2 x 1/2 (b+1)(1/2b) = 15
(b+1)(1/2b)=15
1/2b^2 +1/2b = 15
1/2b^2 + 1/2b - 15 = 0
b^2 + b - 30 = 0
(b+6)(b-5) = 0 so b = base = -6 or 5 (-6 won't work as a measurement so the answer is 5) the height is (b+1) = 6
Wish I could draw a diagram...it would be clearer!
