Question
The height of a triangle is 4 centimeters less than twice the length of its base. If the total area of the triangle is 48 square centimeters, then find the lengths of the base and height.
Answers
Reiny
base ----- x cm
height ---- 2x-4 cm
area of triangle = (1/2) base x height
(1/2)(x)(2x-4) = 48
x(2x-4) = 96
2x^2 - 8x - 96 = 0
x^2 - 4x - 48 = 0
(x-8)(x+6) = 0
x = 8 or x = -6, the latter is inadmissable
base is 8 cm
height is 12 cm
height ---- 2x-4 cm
area of triangle = (1/2) base x height
(1/2)(x)(2x-4) = 48
x(2x-4) = 96
2x^2 - 8x - 96 = 0
x^2 - 4x - 48 = 0
(x-8)(x+6) = 0
x = 8 or x = -6, the latter is inadmissable
base is 8 cm
height is 12 cm