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

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Joined: 02 Sep 2009
Posts: 53066
In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What  [#permalink]

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09 Oct 2018, 22:35
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Difficulty:

25% (medium)

Question Stats:

75% (01:38) correct 25% (01:38) wrong based on 32 sessions

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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 [ 18.09 KiB | Viewed 415 times ]

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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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10 Oct 2018, 00:51
Bunuel wrote:

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 $$= AB*BC = 4*9 = 36$$

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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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13 Oct 2018, 17:32
Bunuel wrote:

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.

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Re: In the figure, ABCD is a rectangle, and the area of ∆ACE is 10. What   [#permalink] 13 Oct 2018, 17:32
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