GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 10:36

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47037
In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

Show Tags

12 Aug 2017, 16:22
00:00

Difficulty:

15% (low)

Question Stats:

100% (00:41) correct 0% (00:00) wrong based on 50 sessions

HideShow timer Statistics

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

Attachment:

2017-08-13_0320.png [ 5.35 KiB | Viewed 1221 times ]

_________________
SC Moderator
Joined: 22 May 2016
Posts: 1826
In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

Show Tags

12 Aug 2017, 16:55
Bunuel wrote:

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

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

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2934
Location: India
GPA: 3.12
Re: In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

Show Tags

12 Aug 2017, 18:07

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
_________________

You've got what it takes, but it will take everything you've got

Intern
Joined: 26 Oct 2015
Posts: 3
Re: In the figure above, what is the perimeter of ∆ ABC in terms of m? [#permalink]

Show Tags

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

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.