shankar.ashwin wrote:If an isosceles right triangle has an area of 2x² + 2x + 1/2, what is its perimeter?
A) 3(x+1)
B) √2(x²+1)
C) (2x-1)(2x+1)
D) (2+√2) (2x+1)
E) 2x + √2
In an isosceles right triangle, the sides are proportioned s : s : s√2.
Since s is both the base and the height, area = (1/2)s².
Let x=1.
Area = 2x² + 2x + 1/2 = 2(1)² + 2(1) + 1/2 = 9/2.
Thus:
(1/2)s² = 9/2.
s = 3.
p = 3 + 3 + 3√2 = 6 + 3√2. This is our target.
Now we plug x=1 into the answers to see which yields our target of 6 + 3√2.
Only answer choice
D works:
(2+√2) (2x+1) = (2+√2) (2*1+1) = (2+√2) (3) = 6 + 3√2.
The correct answer is
D.
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