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05 Oct 2017, 01:43
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E
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Difficulty:
35%
(medium)
Question Stats:
76% (01:56) correct
24%
(02:26)
wrong
based on 59
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The triangular portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals
(A) √13
(B) 2√13
(C) 6
(D) 8
(E) 10
Attachment:
2017-10-04_1126.png [ 6.1 KiB | Viewed 2542 times ]
05 Oct 2017, 02:16
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Area of flower bed = (1/2)*x*y = 24, or xy=48 ----(1)
also we know that x=y+2 ----(2)
solving eq. (1) and (2), we get y=-8 and y=6, but cannot be negative, so we have y=6 and hence x = y+2 = 8
Now applying Pythagoras theorem, we get: Z^2 = x^2 + y^2 = 8^2 + 6^2 = 64+36 =100
and hence z=10
also we know that x=y+2 ----(2)
solving eq. (1) and (2), we get y=-8 and y=6, but cannot be negative, so we have y=6 and hence x = y+2 = 8
Now applying Pythagoras theorem, we get: Z^2 = x^2 + y^2 = 8^2 + 6^2 = 64+36 =100
and hence z=10
05 Oct 2017, 07:35
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Area of the triangular bed = 1/2 xy = 24 => xy = 48
x=y+2 =>x-y=2
The triangular flower bed is a right angled triangle.
By Pythagoras theorem, \(x^2+y^2=z^2\)
z=\(\sqrt{x^2+y^2}\) = \(\sqrt{(x-y)^2+2xy}\)
=\(\sqrt{2^2+2*48}\)=\(\sqrt{100}\)
=10
Answer E
x=y+2 =>x-y=2
The triangular flower bed is a right angled triangle.
By Pythagoras theorem, \(x^2+y^2=z^2\)
z=\(\sqrt{x^2+y^2}\) = \(\sqrt{(x-y)^2+2xy}\)
=\(\sqrt{2^2+2*48}\)=\(\sqrt{100}\)
=10
Answer E
