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In trapezium ABCD, AB||CD and AC = BD. If area of the

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Bijesh
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In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink] New post   30 Jul 2019, 05:00
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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
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D
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Vyshak
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Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink] New post   10 Aug 2019, 22:51
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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
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Bijesh
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Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink] New post   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



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
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Vyshak
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Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink] New post   12 Aug 2019, 09:20
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AB + CD = 12

If CD = x, AB = 12 - x

CD = EF = x

AE + FB = AB - EF = 12 - x - x = 12 - 2x

But AE = FB as the two triangles CAB and ADB are congruent(Side Angle Side).

Since AE = FB, AE + AE = 2AE = 12 - 2x --> AE = 6 - x

FB = 6 - x

Bijesh wrote:
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
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gmatclubot
Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink]
12 Aug 2019, 09:20
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