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

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

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New post 21 Dec 2018, 02:37
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

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

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

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

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New post 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
      o Breadth, EF = 2

    • 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

Answer: 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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