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Right triangle ABC and rectangle EFGH have the same perimeter. What is

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Math Expert
Joined: 02 Sep 2009
Posts: 58377
Right triangle ABC and rectangle EFGH have the same perimeter. What is  [#permalink]

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21 Dec 2018, 02:37
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Difficulty:

15% (low)

Question Stats:

82% (00:28) correct 18% (01:34) wrong based on 31 sessions

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Right triangle ABC and rectangle EFGH have the same perimeter. What is the value of x?

A. 2
B. 3
C. 4
D. 5
E. 6

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Capture (6).JPG [ 23.9 KiB | Viewed 395 times ]

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Re: Right triangle ABC and rectangle EFGH have the same perimeter. What is  [#permalink]

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21 Dec 2018, 03:18
third side of triangle is 5 ; perimeter of triangle is 5+4+3= 12

so 2(2+x)=12
x= 4 IMO C

Bunuel wrote:

Right triangle ABC and rectangle EFGH have the same perimeter. What is the value of x?

A. 2
B. 3
C. 4
D. 5
E. 6

Attachment:
Capture (6).JPG
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Right triangle ABC and rectangle EFGH have the same perimeter. What is  [#permalink]

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21 Dec 2018, 05:56

Solution

Given:
ABC is a right-angled triangle
o Perpendicular sides, AB and AC = 3 and 4 respectively

• EFGH is a rectangle

• Perimeter of ABC = perimeter of EFGH

To find:
• The length of rectangle, x

Approach and Working:
$$BC = √(3^2 + 4^2) = √25 = 5$$
• Perimeter of triangle ABC = 3 + 4 + 5 = 12
• Perimeter of rectangle = 2 * (2 + x)

We are given that, 2 * (2 + x) = 12
• Thus, x = 6 – 2 = 4

Hence, the correct answer is Option C

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Right triangle ABC and rectangle EFGH have the same perimeter. What is   [#permalink] 21 Dec 2018, 05:56
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