Question

The area of triangle ABC ABC is 18 cm2. Side AC=4x AC = 4 x and side AB=x+3 AB = x + 3 . Given that angle A=30∘ , calculate the value of x

Answer 1

Answer:

x = 3

Step-by-step explanation:

Let the altitude from B to AC intersect at point D.  Then BD is a height of the triangle with base AC

ΔABD is a 30-60-90 triangle since m∠A = 30

Therefore, AB = 2(BD)  or BD = AB/2 = (x+3)/2

Area of the triangle = bh/2 = AC(BD)/2 = 4x(x + 3)/(2)(2)

= x(x + 3) = 18

$x^{2} + 3x = 18$

$x^{2} + 3x - 18 = 0$

(x + 6)(x - 3) = 0

x = -6  or x = 3

x cannot equal -6, so x = 3