AnkitK wrote:
If an isosceles triangle an area of 2x^2+2x+1/2.What is its perimeter?
A.3(x+1)
B.2^1/2(x^2+1)
C.(2^1/2 x-1)(2x+1)
D.(2+2^1/2)(2x+1)
E.2x+2^1/2
I think there is some mistake in typing the question, you can not answer this question unless it is
RIGHT ANGLED ISOSCELES TRIANGLE Now, if we take the correction into consideration then following will be the diagram
Attachment:
D.jpg [ 24.33 KiB | Viewed 2443 times ]
Now, In the given triangle AB = BC ...isosceles triangle
Hence angle A = angle C = 45
And angle B = 90
Now area of triangle = 1/2 *AB* BC
thus \(2x^2+2x+1/2 = 1/2 * AB^2\)
Hence \(AB^2 = 4x^2+4x+1\)
\(AB^2 = (2x+1)^2\)
Hence AB=BC = 2x+1
Now AC is an hypotenuse of the triangle
hence AC = 2^1/2 AB = 2^1/2 (2x+1)
Now perimeter = 2AB + AC = 2 (2x+1) + 2^1/2 (2x+1)
= (2x+1) (2+2^1/2)
Hence Option D is an answer