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In the figure above, the perimeter of rectangle ABCD is 30  [#permalink]

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In the figure below, the perimeter of rectangle ABCD is 30, and the ratio of length to width is 2:1. If CE = 2/5 CD, what is the area of triangle AED ?

A. 30
B. 25
C. 20
D. 15
E. 10

Originally posted by guerrero25 on 30 Jul 2014, 07:15.
Last edited by Bunuel on 30 Jul 2014, 07:26, edited 1 time in total.
Edited the question
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: In the figure above, the perimeter of rectangle ABCD is 30  [#permalink]

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guerrero25 wrote: In the figure below, the perimeter of rectangle ABCD is 30, and the ratio of length to width is 2:1. If CE = 2/5 CD, what is the area of triangle AED ?

A. 30
B. 25
C. 20
D. 15
E. 10

The perimeter = 2(length + width). Since he ratio of length to width is 2:1 and the permittee is 30, then 2(2*width + width) = 30 --> width = 5 and length = 10.

CE = 2/5 CD = 2/5*width = 2, thus DE = width - CE = 3.

The area of triangle AED = 1/2*base*height = 1/2*length*CE = 1/2*10*3 = 15.

Hope it's clear.
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Re: In the figure above, the perimeter of rectangle ABCD is 30  [#permalink]

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Refer diagram below; We require to find the area of shaded region

If AB = CD = x, other side would be 15-x (Perimeter = 30)

CE $$= \frac{2x}{5}$$ , so DE $$= \frac{3x}{5}$$

$$\frac{15-x}{x} = \frac{2}{1}$$

x = 5

Area of shaded region$$= \frac{1}{2} * 3 * \frac{5}{5} * 10 = 15$$

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Re: In the figure above, the perimeter of rectangle ABCD is 30  [#permalink]

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_________________ Re: In the figure above, the perimeter of rectangle ABCD is 30   [#permalink] 28 Mar 2018, 17:19
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