The area of ∆cdf is square meters.

Amauri J.

asked • 02/17/22

Type the correct answer in the box.

The diagram shows a section of a bridge between the points A and K. The length of line segment

is 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = 2FK. The first pillar, , is 20 meters tall.

The area of ∆CDF is square meters.

1 Expert Answer

Hi Amauri,

Because your triangles are similar, you can set up a proportion to calculate the area of the triangle CDF.

Remember that the area of a triangle is calculated by taking 1/2 of the Height (altitude) x Base

Since 2AC = CF, we know that 2BG = DH, since BG is 20, we know that DH has to be 40. Now to calculate the length of the base CH.

The full length of the bridge is 640 meters, and we know that if we add up all of the lengths it will equal that 640 meters. so let's call the lengths of AC and FK, 2x for simplicity, CF would then be x because of the proportions of these similar triangles. So mathematically we find that 2x + x + 2x = 640 and x would then be 5x=640 (divide by 5) and get x = 128.

So, the base of the triangle we're interested in is 128 and it's height or altitude is 40. Plug that into your formula

A = 1/2 bh

A = 1/2(128)(40)

A = 2,560 square meters

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Algebra -> Triangles -> SOLUTION: The diagram shows a section of a bridge between the points A and K. The length of line segment AK is 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = Log On

The diagram shows a section of a bridge between the points The diagram shows a section of a bridge between th - Gauthmath and K. The length of line segment \overline {AK} is 640 meters. \triangle ABC, \triangle CDF and \triangle FJK are similar, and 2AC=CF=2FK. The first pillar, \overline {BG} , is 20 meters tall. The area of ΔCDFis \square square meters.

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Algebra 90 Online

OpenStudy (mrb.x):

The diagram shows a section of a bridge between the points A and K. The length of line segment AK is 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = 2FK. The first pillar, BG, is 20 meters tall. The area of ∆CDF is ___square meters.

6 years ago

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OpenStudy (mrb.x):

@KendrickLamar2014

6 years ago

OpenStudy (anonymous):

in order to find the area you need values of "CF" and "DH"... from 2AC = CF = 2FK and the fact that AK = AC+CF+FK ... we should be able to get CF... Also, as the triangles are similar that should help in getting DH given BG is 20m... Does that help ??

6 years ago

OpenStudy (mrb.x):

Not at all. I'm really bad at this stuff, I'm making a 68 in math models and I can't pass this application to finish. I've failed this I dont know how many times.

6 years ago

OpenStudy (anonymous):

lets take it step by step: from 2AC = CF = 2FK and the fact that AK = AC+CF+FK ... we should be able to get CF... Can you explain what you understood from this ?

6 years ago

Join the QuestionCove community and study together with friends!

OpenStudy (mrb.x):

I dont understand how to do this since we dont have the measurements.

6 years ago

OpenStudy (anonymous):

do you agree that AK = AC+CF+FK ???

6 years ago

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