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In trapezium ABCD, AB||CD and AC = BD. If area of the
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30 Jul 2019, 05:00
30 Jul 2019, 05:00
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28% (01:35) correct
71% (01:57) wrong based on 7 sessions
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In trapezium ABCD, AB||CD and AC = BD. If area of the trapezium is 60 sq units and height of the trapezium is 10 units, what is the length of diagonal BD?
A) 10 units
B)\(\sqrt{116}\) units
C) 5\(\sqrt{5}\) units
D) \(\sqrt{136}\)
E) 12 units
Source: Jamboree Green Book 1
A) 10 units
B)\(\sqrt{116}\) units
C) 5\(\sqrt{5}\) units
D) \(\sqrt{136}\)
E) 12 units
Source: Jamboree Green Book 1
Re: In trapezium ABCD, AB||CD and AC = BD. If area of the
[#permalink]
10 Aug 2019, 22:51
10 Aug 2019, 22:51
2
Area = 60
0.5(AB + CD)(10) = 60
AB + CD = 12
From the below figure, we have
CD = EF = x
AB = 12 - x
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
Triangle DEB is right angled --> BD^2 = 100 + 36 = 136
BD = sqrt(136)
Answer: D
0.5(AB + CD)(10) = 60
AB + CD = 12
From the below figure, we have
CD = EF = x
AB = 12 - x
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
Triangle DEB is right angled --> BD^2 = 100 + 36 = 136
BD = sqrt(136)
Answer: D
Attachments
Trapezium.png [ 12.29 KiB | Viewed 3759 times ]
Re: In trapezium ABCD, AB||CD and AC = BD. If area of the
[#permalink]
11 Aug 2019, 05:49
11 Aug 2019, 05:49
Vyshak wrote:
Area = 60
0.5(AB + CD)(10) = 60
AB + CD = 12
From the below figure, we have
CD = EF = x
AB = 12 - x
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
Triangle DEB is right angled --> BD^2 = 100 + 36 = 136
BD = sqrt(136)
Answer: D
0.5(AB + CD)(10) = 60
AB + CD = 12
From the below figure, we have
CD = EF = x
AB = 12 - x
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
Triangle DEB is right angled --> BD^2 = 100 + 36 = 136
BD = sqrt(136)
Answer: D
Could u elaborate from :
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
