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21 Nov 2022, 00:53
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (02:46) correct
52%
(02:13)
wrong
based on 25
sessions
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A plot of land used to display flowers in a botanical garden was designed in the shape of a trapezoid in which the lengths of the two sides that are not parallel are equal. The length of the longer parallel side is 5 times the length of the shorter parallel side, and the distance between the two parallel sides is 3 times the length of the shorter parallel side. The perimeter of the plot is 135 meters. Approximately what is the length, in meters, of the shorter parallel side?
A. 9
B. 10
C. 11
D. 12
E. 13
A. 9
B. 10
C. 11
D. 12
E. 13
26 Nov 2022, 11:23
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Bunuel
Attachment:
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\(4x^2 +9x^2 =h^2\)
\(13x^2 = h^2\)
\(h=x\sqrt13\)
Also we know perimeter \(= 135\), so:
\(x\sqrt13 + x\sqrt13 +x +5x =135 \)
\(2x\sqrt13 +6x =135\) ...(i)
\(3 <\sqrt13 <4\)
Lets take \(\sqrt13 = 3\)
Then (i) becomes \(6x +6x =135 \) and solving further we get \( x=11.25 \)
If we take\( \sqrt13 = 4\) then (i) becomes \(8x+6x =135 \) and \(x= 9.6 \)
We can see that as the value of \(\sqrt13\) increases \(x\) decreases and as the value of \(\sqrt13\) decreases \(x\) increases .
So we know \(\sqrt13\) is just less than \(4\) then \(x \) will increase and will be just more than \(9.6\) , Hence nearest option greater than \(9.6\) is \(10\).
Ans B
Hope it's clear.
