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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
Attachment:
2020-10-27_12-28-50.png [ 24.52 KiB | Viewed 5286 times ]
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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
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
RSTQ is a rhombus. The sides of RSQT=((6/2)^+(8/2)^2)^(1/2)=5
The perimeter of RSTQ=4*5=20 B)
The perimeter of RSTQ=4*5=20 B)
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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
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
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.
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.
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
Side of Rhombus RSQT is hypotonus of each right angled triangle and = 5, so perimeter => 4 x 5 = 20, hence B
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Bunuel
\(△DQT = △STC = △RBS = △AQR (3-4-5 △)\)
So, Perimeter all 4 small triangles is \(4*5=20\), Answer must be (B)
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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
Posted from my mobile device
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
Posted from my mobile device
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Posts: 723
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
_________________
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
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Posts: 8
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
Each of the 4 triangles formed is a Pythagorean triplet 3,4,5
Perimeter of RSTQ = 5x4 = 20
Option B
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 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
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