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In the figure above, what is the perimeter of ∆ ABC in terms of m?

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In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

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New post 12 Aug 2017, 16:22
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In the figure above, what is the perimeter of ∆ ABC in terms of m?

(A) 10m
(B) 15m
(C) 17m
(D) 7m + 3√2 m
(E) 12m + 3√2 m


[Reveal] Spoiler:
Attachment:
2017-08-13_0320.png
2017-08-13_0320.png [ 5.35 KiB | Viewed 428 times ]
[Reveal] Spoiler: OA

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In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

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New post 12 Aug 2017, 16:55
Bunuel wrote:
Image
In the figure above, what is the perimeter of ∆ ABC in terms of m?

(A) 10m
(B) 15m
(C) 17m
(D) 7m + 3√2 m
(E) 12m + 3√2 m

[Reveal] Spoiler:
Attachment:
2017-08-13_0320.png

Let X be the point where B intersects side AC

Left triangle ABX is right isosceles (45-45-90) with side ratio \(x: x: x\sqrt{2}\)

3m corresponds with x
Hypotenuse, side AB, therefore is 3\(\sqrt{2}\)m

Triangle BCX, on the right, is 3-4-5 triangle. Hypotenuse, side BC, is 5m

Perimeter = sum of three side lengths

5m + 7m + 3\(\sqrt{2}\)m =

12m + 3\(\sqrt{2}\)m

Answer E

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Re: In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

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New post 12 Aug 2017, 18:07
Image

The triangle to the left is an isosceles right triangle which has
sides in the ratio \(1:1:\sqrt{2}\).
Similarly, the triangle is a right angled triangle with sides
in the ratio of the Pythagorean triplet(3:4:5)

Hence, the hypotenuse of the triangle on the left is \(3\sqrt{2}\)
where as the hypotenuse of the triangle to the right is 5m.

Hence, the perimeter of the triangle is \(5m+4m+3m\)+\(3\sqrt{2}\)m = \(12m\) + \(3\sqrt{2}\)m
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Re: In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

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New post 12 Aug 2017, 22:00
let in the triangle ABC, where the line from B meets line AC be E.

So,
in triangle BCE,hypotenuse BC =(3^2+4^2)^1/2=(9+16)^1/2=25^1/2=5
Here 5M, as the lengths are given terms of M.

for the triangle,
ABE,

AB =(3^2+3^2)^1/2
=(18)^1/2
=3√2
I.E 3√2M

HENCE PERIMETER: BC +AB +AC=5M+3√2M+3M+4M=(12+3√2)M

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Re: In the figure above, what is the perimeter of ∆ ABC in terms of m?   [#permalink] 12 Aug 2017, 22:00
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In the figure above, what is the perimeter of ∆ ABC in terms of m?

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