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What is the area of RST ?

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What is the area of RST ? [#permalink]

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New post 31 May 2018, 12:01
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (00:23) correct 10% (01:32) wrong based on 73 sessions

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Re: What is the area of RST ? [#permalink]

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New post 31 May 2018, 13:14
Bunuel wrote:
Image
What is the area of RST ?


A. 6

B. \(2 \sqrt{13}\)

C. 10

D. 12

E. 24




Attachment:
RST.jpg



Coordinate of R (6,0), S(6,4) and O(0,0)

Length of RO = sqrt[(0-6)^2 + (0-0)^2] = 6
Length of SR = sqrt[(6-6)^2 + (4-0)^2] = 4

RO = ST

Therefore the area of triangle RST = 1/2 * 6 * 4 = 12
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Re: What is the area of RST ? [#permalink]

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New post 01 Jun 2018, 03:13

Solution



To find:
• The area of the triangle RST

Approach and Working:
• As SR is perpendicular to x axis and ST is perpendicular to y axis, the coordinates of point S represents the distance of the point S from x axis and y axis respectively
    o Distance of S from x axis = 6 unit
    o Distance of S from y axis = 4 unit
• RST is a right-angled triangle, therefore the area of RST = ½ * SR * ST = ½* 4 * 6 = 12 sq. unit
Hence, the correct answer is option D.

Answer: D

[In other way, the line RT is the diagonal of the rectangle ORST. Hence, area of triangle RST = ½ of area of rectangle ORST = ½ * 6 * 4 = 12]
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Re: What is the area of RST ? [#permalink]

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New post 01 Jun 2018, 03:44
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Bunuel wrote:
Image
What is the area of RST ?


A. 6

B. \(2 \sqrt{13}\)

C. 10

D. 12

E. 24


Attachment:
RST.jpg


Area of the triangle = (1/2) Base * Height
Here base of RST = ST = 6 (x-Co-ordinate of Point S)
Here Height of RST = RS = 4 (Y-Co-ordinate of Point S)

Hence, Area= (1/2)*4*6 = 12

Answer: option D
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Re: What is the area of RST ? [#permalink]

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New post 01 Jun 2018, 03:58
OA: D
Area of rectangle 0RST =\(6*4 =24\)

Quote:
Each diagonal divides the rectangle into two congruent right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the rectangle

Area of \(\triangle\) RST=\(\frac{1}{2}*24=12\)
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Re: What is the area of RST ? [#permalink]

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New post 03 Jun 2018, 18:23
Bunuel wrote:
Image
What is the area of RST ?


A. 6

B. \(2 \sqrt{13}\)

C. 10

D. 12

E. 24


Attachment:
RST.jpg


We see that leg TS = 6 and leg SR = 4. Thus, the area is 6 x 4 x 1/2 = 12.

Answer: D
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Re: What is the area of RST ? [#permalink]

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New post 04 Jun 2018, 02:22
Bunuel wrote:
Image
What is the area of RST ?


A. 6

B. \(2 \sqrt{13}\)

C. 10

D. 12

E. 24


Attachment:
RST.jpg


Let 'O' be the origin of the given xy-plane.

so, ORST is an rectangle with length,OR=TS=6 unit and breadth,OT=SR=4 unit

Now, required area of triangle RST=\(\frac{1}{2}\)* Area of rectangle ORST=\(\frac{1}{2}\)*TS*SR=\(\frac{1}{2}\)*6*4=12

Hence, Option(D) is correct.
Re: What is the area of RST ?   [#permalink] 04 Jun 2018, 02:22
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