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

Question

3 years ago

6

value of x

1 answer:

harina [27] · Answer 1 · 2022-04-18T07:09:05+03:00

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