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Find the area of triangle $QST$

0

1

$begingroup$

In triangle $PQR$, $U$ is a point on $PR$, $S$ is a point on $PQ$, $T$ is a point on $QR$ with $US$ being parallel to $RQ$, and $UT$ is parallel to $PQ$.
The area of $PSU$ is $120 in^2$ and the area of triangle $TUR$ is $270 in^2$.
The area of $QST$ in $in^2$, is

Diagram

This is a multiple choice question

$A) 150$

$B) 160$

$C) 170$

$D) 180$

$E) 200$

I figure triangle $STU$ being equal to triangle $QST$ but $SU$ is not confirmed as equal to $QT$. Is there any way to confirm the lengths, maybe if I separate the areas of the two triangles to experiment with proportions since the two triangles with area have parallel sides equal to each other.

triangles problem-solving

share|cite|improve this question

edited Mar 27 at 17:59

JC2000

518

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1

New contributor

Andrei Lenedin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
  $endgroup$
  – José Carlos Santos
  Mar 26 at 10:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  When $US parallel RQ$ and $UT parallel PQ$, $UTQS$ will be a parallelogram. This means $|SU| = |QT|$.
  $endgroup$
  – achille hui
  Mar 27 at 18:24
  
  

  
  
  
  

add a comment | 

0

1

$begingroup$

In triangle $PQR$, $U$ is a point on $PR$, $S$ is a point on $PQ$, $T$ is a point on $QR$ with $US$ being parallel to $RQ$, and $UT$ is parallel to $PQ$.
The area of $PSU$ is $120 in^2$ and the area of triangle $TUR$ is $270 in^2$.
The area of $QST$ in $in^2$, is

Diagram

This is a multiple choice question

$A) 150$

$B) 160$

$C) 170$

$D) 180$

$E) 200$

I figure triangle $STU$ being equal to triangle $QST$ but $SU$ is not confirmed as equal to $QT$. Is there any way to confirm the lengths, maybe if I separate the areas of the two triangles to experiment with proportions since the two triangles with area have parallel sides equal to each other.

triangles problem-solving

share|cite|improve this question

edited Mar 27 at 17:59

JC2000

518

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1

New contributor

Andrei Lenedin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
  $endgroup$
  – José Carlos Santos
  Mar 26 at 10:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  When $US parallel RQ$ and $UT parallel PQ$, $UTQS$ will be a parallelogram. This means $|SU| = |QT|$.
  $endgroup$
  – achille hui
  Mar 27 at 18:24
  
  

  
  
  
  

add a comment | 

$begingroup$

In triangle $PQR$, $U$ is a point on $PR$, $S$ is a point on $PQ$, $T$ is a point on $QR$ with $US$ being parallel to $RQ$, and $UT$ is parallel to $PQ$.
The area of $PSU$ is $120 in^2$ and the area of triangle $TUR$ is $270 in^2$.
The area of $QST$ in $in^2$, is

Diagram

This is a multiple choice question

$A) 150$

$B) 160$

$C) 170$

$D) 180$

$E) 200$

I figure triangle $STU$ being equal to triangle $QST$ but $SU$ is not confirmed as equal to $QT$. Is there any way to confirm the lengths, maybe if I separate the areas of the two triangles to experiment with proportions since the two triangles with area have parallel sides equal to each other.

triangles problem-solving

share|cite|improve this question

edited Mar 27 at 17:59

JC2000

518

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1

New contributor

Andrei Lenedin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 27 at 17:59

JC2000

518

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1

New contributor

Andrei Lenedin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 27 at 17:59

JC2000

518

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1

New contributor

Andrei Lenedin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Mar 27 at 17:59

JC2000

518

edited Mar 27 at 17:59

JC2000

518

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1

New contributor

Andrei Lenedin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 26 at 9:58

Andrei LenedinAndrei Lenedin

1