In the figure below, K and J lie on triangle ABC, JK is parallel to AB

Question

In the figure below, K and J lie on triangle ABC, JK is parallel to AB, and the lengths of the sides of quadrilateral ABKJ are in inches as indicated. What is the perimeter of triangle ABC ?

(A) 296 inches
(B) 320 inches
(C) 345 inches
(D) 365 inches
(E) 410 inches

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Official Answer

C

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • A triangle ABC, in which points K and J lie on the sides BC and AC such that JK || AB
• JK = 60, AJ = 48, BK = 50, and AB = 100

To find  
We need to determine
 • The perimeter of the triangle ABC

Approach and Working out  
As JK || AB, we can say the triangles CJK and CAB are similar to each other.
 • Hence, we can say that CJ/CA = CK/CB = JK/AB = 60/100 = 3/5

If CJ/CA = 3/5, then CJ/(CJ + AJ) = 3/5
 Or, 5CJ = 3CJ + 3AJ
Or, 2CJ = 3 x 48
Or, CJ = 72

Similarly, if CK/CB = 3/5, then CK/(CK + BK) = 3/5
 Or, 5CK = 3CK + 3BK
Or, 2CK = 3 x 50
Or, CK = 75

Hence, the perimeter of the triangle ABC = CJ + AJ + AB + BK + CK = 72 + 48 + 100 + 50 + 75 = 345 inches

Thus, option C is the correct answer.

Correct Answer: Option C

XSatishX · Answer

Whenever a line joins two sides of a triangle and is parallel to the third side, it creates a small triangle similar to the big one. 
Here as well we can prove ABC is similar to JKC.
Angle C is common.
Angle J is equal to Angle A as JK and AB are parallel. (Corresponding Angles)
Angle K is equal to Angle B as JK and AB are parallel. (Corresponding Angles)

Now Triangle ABC is similar to Triangle JKC.
As we know, the sides of two similar triangles will be in a fixed ratio.
JC/AC = KC/BC = JK/AB

Hence we can find the value of JC by Using the equation:
JC/AC = JK/AB
JC/(48+JC) = 60/100
JC =48*60/40 = 72

Similarly 
KC = 50*60/40 = 75

So perimeter of ABC = 100+72+48+50+75 = 345

Answer :  C

ScottTargetTestPrep · Answer

Solution:
 
To determine the perimeter of triangle ABC, we need to determine the lengths of BC and AC (we are already given that AB = 100). Since JK is parallel to AB, triangles JKC is similar to triangle ABC. Since the corresponding sides of similar triangles are proportional. Therefore, we have:

AB/JK = BC/KC

If we let x = KC, we have:

100/60 = (50 + x)/x

5/3 = (50 + x)/x

5x = 150 + 3x

2x = 150

x = 75

Therefore, BC = 50 + 75 = 125.

Likewise, we have:

AB/JK = AC/JC

If we let y = JC, we have:

100/60 = (48 + y)/y

5/3 = (48 + y)/y

5y = 144 + 3y

2y = 144

y = 72

Therefore, BC = 48 + 72 = 120, and hence the perimeter of triangle ABC is 100 + 125 + 120 = 345 inches.

Answer: C

In the figure below, K and J lie on triangle ABC, JK is parallel to AB

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GMAT Problem Solving (PS) Questions

In the figure below, K and J lie on triangle ABC, JK is parallel to AB

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