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In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What

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In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What  [#permalink]

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New post Updated on: 15 Jul 2019, 04:21
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A
B
C
D
E

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Question Stats:

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Originally posted by Bunuel on 09 Oct 2018, 23:35.
Last edited by SajjadAhmad on 15 Jul 2019, 04:21, edited 1 time in total.
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Re: In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What  [#permalink]

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New post 10 Oct 2018, 01:51
Bunuel wrote:
Image
In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What is the area of the rectangle?

(A) 18
(B) 22.5
(C) 36
(D) 44
(E) 45


Attachment:
rect.jpg


Area of triangle ACE \(= (1/2)*CE*AB = (1/2)*5*AB = 10 (Given)\)

i.e. \(AB = 4\)

also, \(BC = 4+5 = 9\)

Area of rectangle \(= AB*BC = 4*9 = 36\)

Answer: Option C
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Re: In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What  [#permalink]

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New post 13 Oct 2018, 18:32
Bunuel wrote:
Image
In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What is the area of the rectangle?

(A) 18
(B) 22.5
(C) 36
(D) 44
(E) 45


Attachment:
rect.jpg


We can let AB = DC = n, which is the height of triangle ACE if we considered EC as the base. Thus, we have:

½ x 5 x n= 10

2.5n = 10

n = 4

So the area of ABCD is 4 x 9 = 36.

Answer: C
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Re: In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What   [#permalink] 13 Oct 2018, 18:32
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