Question

The sides of an equilateral triangle are (2a - b + 5), (a + b) and (2b - a + 2). What is the area of the triangle?

• A. $\frac{\sqrt{3}}{4}\times a^2$
• B. $\frac{\sqrt{3}}{4}\times b^2$
• C. $\frac{\sqrt{3}}{4}\times 49$
• D. $\frac{\sqrt{3}}{4}\times 81$

Answer 1

The correct option is C

$\frac{\sqrt{3}}{4}\times 49$

$\Delta ABC$ is an equilateral triangle.
$\Rightarrow$ AB = BC = CA

Now AB = BC gives
2b - a + 2 = a + b
$\Rightarrow$ b = 2a - 2 ....... (i)
BC = CA gives
a + b = 2a - b + 5
from (i)
a + 2a - 2 = 2a - 2a + 2 + 5
$\Rightarrow$ 3a = 9
$\Rightarrow$ a = 3
$\therefore$ b = 2 (3) - 2 = 6 - 2 = 4
$\therefore$ AC = 2 (3) - 4 + 5
= 6 - 4 + 5
= 7
Area of equilateral $\Delta =\frac{\sqrt{3}}{4}(side{)}^2$
$=\frac{\sqrt{3}}{4}(7{)}^2$
$=\frac{\sqrt{3}}{4}\times 49$