Problema Solution
The area of a triangle is equal to ½ (base)(altitude). If the area of a triangular poster is 1260 square centimeters and its altitude is 2 feet shorter than twice its base. Find the lengths of the altitude and base.
Answer provided by our tutors
let
a = the base of the triangle
h = the altitude
A = 1260 cm^2 the area of the triangle
1 ft = 30.48 cm
its altitude is 2 feet shorter than twice its base
h = 2a - 2*30.48
h = 2(a - 30.48)
for the area we have
A = (a*h)/2
(a*h)/2 = 1260
plug h = 2(a - 30.48) into the last equation
(a*2(a - 30.48))/2 = 1260
a(a - 30.48) = 1260
by solving the quadratic equation we find
a = 53.87 cm
click here to see the step by step solution of the quadratic equation
h = 2(a - 30.48)
h = 46.78 cm
the altitude is 46.78 cm and the base is 53.87 cm.