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Geometry problem- OG 11 no. 152

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Senior | Next Rank: 100 Posts
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by crejoc » Wed Jul 01, 2009 1:40 am
The shaded portion of the rectangular lot shown below represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

a) sqrt(13)

b) 2 sqrt(13)

c) 6

d) 8

e) 10

OA: e
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Last edited by crejoc on Wed Jul 01, 2009 2:52 am, edited 1 time in total.
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by gauravgundal » Wed Jul 01, 2009 2:26 am
hi
OA e

Area of flower bed = area of triangle = (1/2)*base*height
24 = (1/2)*x*y
x*y =48
but x = y+2
y^2+2y-48=0
y=6 and x=8
thus by pytha thm
z=10
OA e
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by minhphuoc » Mon Nov 12, 2012 2:58 pm
One way to avoid quadratic equation is:
z^2 = x^2 + y^2 --> z^2 = (y + 2)^2 + y^2 = 2y^2 + 4y + 4 = 2(y^2 + 2y) + 4
we know that 48 = y^2 + 2y. Therefore, z^2 = 2.48 + 4 =100 --> z=10
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