In the figure shown, ABCD is a rectangle, AB = 8, and BC = 6. R, S, T,

Question

https://gmatclub.com/forum/download/file.php?id=58588 In the figure shown, ABCD is a rectangle, AB = 8, and BC = 6. R, S, T, and Q are midpoints of the sides of ABCD. What is the perimeter of RSTQ? A. 18 B. 20 C. 22 D. 24 E. 26 Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 2020-10-27_12-28-50.png

rajatchopra1994 · Answer

Explanation:

AB = 8, and BC = 6. 
Take Triangle RBS
R, S are midpoints of the sides of AB & BC
RB = 4 , BS = 3
So RS =√{(4)^2 + (3)^2 }
RS = 5
Similarly, ST, TQ, QR will be 5
Perimeter of RSTQ = 4(5) = 20

IMO-B

gmatcafe · Answer

RSTQ is a rhombus. The sides of RSQT=((6/2)^+(8/2)^2)^(1/2)=5 
The perimeter of RSTQ=4*5=20 B)

prashant0099 · Answer

R, S are midpoints of the sides of AB & BC
RB = 4 , BS = 3 and angle ABC is 90 degree

so using Pythagoras theorem, RS = 5

hence, the  perimeter of RSTQ will be 20

hence B

Perimeter of RSTQ 20

Biswadip · Answer

From the diagram we can conclude 
QR= RS= ST= QT= 5, as its a rectangle and angles A,B, C, D are right angle.
Thus perimeter of Sqr  QRST = 4*5= 20 units.
So B.

AnkitHRD · Answer

Since RSTQ is touching at midpoints of sides of rectangle, we can clearly see 4 similar right angled triangle with side following 3-4-5.

Side of Rhombus RSQT is hypotonus of each right angled triangle and = 5, so perimeter => 4 x 5 = 20, hence B

Abhishek009 · Answer

△DQT = △STC = △RBS = △AQR (3-4-5 △)

So, Perimeter all 4 small triangles is  4*5=20 , Answer must be (B)

Harsh9676 · Answer

IMO B

The quadrilateral RSTQ divides the rectangle into 4 right angle triangles each in 3:4:5 ratio.

Wash side of the quadrilateral would become the hypotenuse with length 5 to the 4 right angled triangles ..

Perimeter = 4*5 = 20

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akadiyan · Answer

In the figure shown, ABCD is a rectangle, AB = 8, and BC = 6. R, S, T, and Q are midpoints of the sides of ABCD. What is the perimeter of RSTQ?

Given :
AB =8
BC =6
R,S,T,Q are mid points.

Since R is midpoint of AB, we can consider AR=RB=4 , based on this we can also conclude that CT=TD=4
Similarly S is midpoint of BC, we can consider BS=SC=3 , based on this we can conclude that AQ=DQ=3

To identify the length of the 3rd side. 
We have 2 sides AR=4 , AQ=3, now we have 2 sides of a triangle with lengths 3 and 4, so the third side is 5 (3-4-5 triangle)

The length of the side RQ=5
Using the similar calculation, we can calculate the length of other sides to be equal to 5 as well.

So the perimeter of RSTQ = 5+5+5+5 = 20

Ans:  B

BSTEPHANOS · Answer

Knowing that R,S,T,Q are midpoints 
Each of the 4 triangles formed is a Pythagorean triplet 3,4,5
Perimeter of RSTQ = 5x4 = 20

Option B

GCMEMBER · Answer

In the figure shown, ABCD is a rectangle, AB = 8, and BC = 6. R, S, T, and Q are midpoints of the sides of ABCD. What is the perimeter of RSTQ?

In the above figure,
the following triangles are congruent,
QAR = SBR = SCT = QDT

so, QR = RS = ST = TQ = 5
Therefore, perimeter of RSTQ = 5*4= 20 units.

Choice B

In the figure shown, ABCD is a rectangle, AB = 8, and BC = 6. R, S, T,

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In the figure shown, ABCD is a rectangle, AB = 8, and BC = 6. R, S, T,

Prep Toolkit

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