Question 402411
The area of a triangular sign is 33 square meters. the base of the triangle is 1meter less than double the altitude. find the altitude and the base of the sign
.
Let a = altitude
then
2a-1 = base
.
definition of area of any triangle:
(1/2)*base*height
.
(1/2)(2a-1)(a) = 33
(2a-1)(a) = 66
2a^2-a = 66
2a^2-a-66 = 0
(2a-11)(a+6) = 0
a = {11/2, -6}
we can throw out the negative solution leaving
a = 11/2 = 5.5 meters (altitude)
.
Base:
2a-1 = 2(5.5)-1 = 11-1 = 10 meters