GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In trapezium ABCD,AB||CD and AC=BD.Given area and ht,find BD
[#permalink]
23 Sep 2019, 20:57
23 Sep 2019, 20:57
1
00:00
Question Stats:
100% (01:36) correct
0% (00:00) wrong based on 6 sessions
Hide Show timer Statistics
In trapezium ABCD, AB || CD and AC=BD. If area of the trapezium is 60 sq units and height of the trapezium if 10 units, what is the length of diagonal BD?
A) 10 units
B) \(\sqrt{116}\)
C) 5\(\sqrt{5}\)
D) \(\sqrt{136}\)
E) 12 units
Source : Jamboree
A) 10 units
B) \(\sqrt{116}\)
C) 5\(\sqrt{5}\)
D) \(\sqrt{136}\)
E) 12 units
Source : Jamboree
Re: In trapezium ABCD,AB||CD and AC=BD.Given area and ht,find BD
[#permalink]
23 Sep 2019, 22:07
23 Sep 2019, 22:07
3
fdundo wrote:
In trapezium ABCD, AB || CD and AC=BD. If area of the trapezium is 60 sq units and height of the trapezium if 10 units, what is the length of diagonal BD?
A) 10 units
B) \(\sqrt{116}\)
C) 5\(\sqrt{5}\)
D) \(\sqrt{136}\)
E) 12 units
Source : Jamboree
A) 10 units
B) \(\sqrt{116}\)
C) 5\(\sqrt{5}\)
D) \(\sqrt{136}\)
E) 12 units
Source : Jamboree
Here,
Key Point:: When ever the diagonals are equal \(-\) then it is isosceles trapezoid
Meaning as per diagram below \(CN = PD\)
Now,
Given Area of the trapezoid = \(60\) and height \(BP = AN =10\)
or \(60\) = \((\frac{{AB + CD}}{2}) * Height\)
or \(AB + CD = 12\)
or \(AB + NP + x + x = 12\) (Let us take CN = PD = x , since it is a isosceles trapezoid)
or \(AB + NP + 2x = 12\)
or \(NP + NP +2x =12 ( AB =NP)\)
or \(NP + x = 6\)
i.e \(NP + x = ND = 6\)
Now in the \(\triangle\) NAD
\(BD = 6, AN = 10\)
Therefore \(AD\) = \(\sqrt{10^2 + 6^2} = \sqrt136\)
Attachments
Trapezoid.jpg [ 18.99 KiB | Viewed 2104 times ]
gmatclubot
Re: In trapezium ABCD,AB||CD and AC=BD.Given area and ht,find BD [#permalink]
23 Sep 2019, 22:07
Moderators:
