Problema Solution
A carpenter is making a backyard deck. In his measurements, he has determined that he needs to make a support triangle with an area 22 m². He knows that the base must be 1 less than 3 times the height. If the base is represented by 3x - 1 and the height = x, find the dimensions of the triangle.
Write base = ______________ m and height = ______________ m.
Answer provided by our tutors
let
b = 3x - 1 be the base of the triangle
h = x the height of the triangle
A = 22 m^2 is the area of the triangle
A = (b*h)/2 is the formula for the area of the triangle
if substitute b and h in A we get
(3x - 1)*x/2 = 22
3x^2 - x = 44
3x^2 - x - 44 = 0
by solving the quadratic equations we find the roots
x1 = - 11/3
this is not the solution since we need x > 0
x2 = 4 m is the solution that we are looking for
b = 3*4 - 1 = 11 m
h = 4 m
base = 11 m and height = 11 m.