Is it ... or not
It is known that A and B are the lengths of two sides of an isosceles triangle, which satisfies equation 2√(3a-6)+3√(2-a)=b-4. Find the perimeter and area of this isosceles triangle.
If so.
2√(3a-6)+3√(2-a)=b-4
It becomes 2√3*√(a-2) +3√(2-a)=b-4.
A-2≥0, 2-a≥0, so a=2.
Left =0, so b-4=0 and b=4.
And △ABC is an isosceles △. So the perimeter C=4+4+2= 10.
In △ABC, according to the cosine theorem, we can get
cosA=(b? +c? +a? )/2bc=(4? +4? -2? )/(2*4*4)=7/8
Sina =√ 15/ 8
s = 1/2 bcsina = 1/2 * 4 * 4 *√ 15/8 =√ 15