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11 Nov 2017, 06:54
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E
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87% (01:31) correct
13%
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In the figure above, each of the four squares has sides of length x. If ∆ PQR is formed by joining the centers of three of the squares, what is the perimeter of ∆ PQR in terms of x?
(A) 2x√2
(B) (x√2/2) + x
(C) 2x + √2
(D) x√2 + 2
(E) 2x + x√2
Attachment:
2017-11-11_1744_002.png [ 3.82 KiB | Viewed 10527 times ]
E.
from the fig PQ=x and QR=x. hence PR=X*sqrt(2)
so perimeter = x+x+2*Sqrt(x) = 2x + x*sqrt(2)
from the fig PQ=x and QR=x. hence PR=X*sqrt(2)
so perimeter = x+x+2*Sqrt(x) = 2x + x*sqrt(2)
11 Nov 2017, 17:37
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Bunuel
If centers of squares with side length x are joined, then
Horizontally, Side PQ =
\(\frac{1}{2}x + \frac{1}{2}x = x\)
Vertically, side QR =
\(\frac{1}{2}x + \frac{1}{2}x = x\)
We have an isosceles right triangle, angle measures are 45-45-90, sides lengths are in ratio \(x : x : x\sqrt{2}\)
Side PR corresponds with
\(x\sqrt{2}\)
Equal sides' length each =\(x\)
PR=\(x\sqrt{2}\)
Perimeter = \((x + x + x\sqrt{2}) =(2x + x\sqrt{2})\)
Answer E
Sasindran , maybe I don't understand your math language, but think you mean: x*sqrt(2), not, as is written, 2*sqrt(x)
