Question

The sides of an equilateral triangle are (a + 2b), (a + 2b + 1 ) and (2a - b), then the area of the triangle will be?

Answer 1

Sir,

the above question states that the triangle is Equilateral.

Thus, all of its sides must be Equal.

But the 1st and the 2nd lengths provided are cannot be equal ...

as the terms (a + 2b) are common with a (+1) in the second which clearly shows the inequality in the lengths.......

Pleas check the question again if it might be a typing mistake.

Regards,

Ansh Shah (IX)

Answer 2

Answer:

$25 \sqrt{3} / 64$ sq. units

Step-by-step explanation:

Given that the tritriangle is equilateral :

a+2b = a-2b+1 = 2a-b

a+2b = 2a-b                                      a-2b+1 = 2a - b

3b = 2a - a                                         a= 2a - b + 2b - 1

3b = a                                                a- 2a = b - 1

                                                         -1a= b - 1

                                                          a = 1 - b

3b = 1 - b                                           a = 1 - 1/4 = 3/4

3b + b = 1                                           therefore ; a = 3/4

4b = 1

therefore ; b = 1/4  

a = 3/4

Side = a + 2b     ( all sides are equal in equilateral triangle )

3/4 + 2 * $3/4 + 2 * 1/4 \\= 3+2/4 \\= 5/4$                                

Area = $\sqrt{3} / 4 ( side)$²

$\sqrt{3} / 4 * (5/4)^{2} \\=\sqrt{3} / 4 * 25/16\\=25 \sqrt{3} / 64$

threrefore ; answer is

$25 \sqrt{3} / 64$ sq. units