Problema Solution
The front of an A-frame cabin in a national park is in the shape of a triangle with an area of 33 ft^2. If the height is 1 less than twice the base, find the base and height of the front of the cabin.
Answer provided by our tutors
let
a = the length of the base, a>0
h = the length of the height, h>0
A = 33 ft^2 the area of the triangle
the height is 1 less than twice the base:
h = 2a - 1
the triangle has an area of 33 ft^2:
A = (1/2)ah
(1/2)ah = 33
plug h = 2a - 1 into the last equation:
(1/2)a(2a - 1) = 33
by solving we find:
a = 6 ft
click here to see the step by step solution of the equation:
h = 2*6 - 1
h = 11 ft
the base is 6 ft and height is 11 ft.