# GMAT question 146

#### ironsheep

##### Junior Member
This is GMAT question is from GMAT Official Guide 2019 Quantitative Review and the figure and word problem is in the image--- if you can't see it, then can someone make the picture look nice( I know someone on this forum knows how to do that somehow??). The answer is C

I used A squared + B squared = C squared

I did RS squared + ST squared = RT squared. That means 4 squared + 5 squared = 41. That means RT equals Square root of 41. Then you do RT squared plus QR squared = QT squared. 41 + 4 = 45 squared. QT = square root 45. Then you use PQ now and with QT you can find PT.

3 squared = 9. 9 plus PT squared = QT squared. Pt squared equals 36 and PT equals 6. PT equals 6, so how can I answer this question??

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#### Jomo

##### Elite Member
Can you tell me when you are allowed to use A squared + B squared = C squared? What are A B and C?

#### ironsheep

##### Junior Member
A squared plus B squared = C squared is a forumula used for triangles. You divide the image they give you into three triangles.

#### Jomo

##### Elite Member
A squared plus B squared = C squared is a forumula used for triangles. You divide the image they give you into three triangles.
What you said is not entirely true. That equation ONLY works for RIGHT triangles. You never answered what A B and C were!!! A and B are the two legs of a right triangle. C is the hypotenuse of the triangle (which is the angle opposite the right angle).
Try something else unless you can find right angle(s)

#### Jomo

##### Elite Member
A squared plus B squared = C squared is a forumula used for triangles. You divide the image they give you into three triangles.
How are you deciding which side is C????

#### ironsheep

##### Junior Member
If I can't use A squared + B squared = C squared, then how will i find PT. Since it "Not drawn to scale", then it could be 5, 10, and 15!!! How else do you find the side of a triangle??

#### Jomo

##### Elite Member
I did RS squared + ST squared = RT squared. That means 4 squared + 5 squared = 41.
Why not RT2= RS2 + ST2?
Do you see why you need to pick A B and C correctly.

#### Jomo

##### Elite Member
If I can't use A squared + B squared = C squared, then how will i find PT. Since it "Not drawn to scale", then it could be 5, 10, and 15!!! How else do you find the side of a triangle??
I think that you need to use the following fact: In a triangle the largest side is opposite the largest angle, the smallest side is opposite the smallest angle ....

Here is a better hint. You have a triangle that has two sides of length r and s (assume r<.s) The length of the 3rd side is between s-r and s+r

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#### ironsheep

##### Junior Member
Why not RT2= RS2 + ST2?
Do you see why you need to pick A B and C correctly.

I did do RT = RS squared + ST squared--- RT squared = 16 + 25= 41 squared. Answer square root of 41.

Then you go further with
I did RS squared + ST squared = RT squared. That means 4 squared + 5 squared = 41. That means RT equals Square root of 41. Then you do RT squared plus QR squared = QT squared. 41 + 4 = 45 squared. QT = square root 45. Then you use PQ now and with QT you can find PT.

3 squared = 9. 9 plus PT squared = QT squared. Pt squared equals 36 and PT equals 6. PT equals 6, so how can I answer this question??

#### Jomo

##### Elite Member
Based on the theorem above what can the length of PR range from? How about TR? Now what is the range of PT? Now use the range of PT to determine the answer.

#### ironsheep

##### Junior Member
Based on the theorem above what can the length of PR range from? How about TR? Now what is the range of PT? Now use the range of PT to determine the answer.
???? What do you mean, "range of PT?""

#### Jomo

##### Elite Member
I did do RT = RS squared + ST squared--- RT squared = 16 + 25= 41 squared. Answer square root of 41.

Then you go further with
I did RS squared + ST squared = RT squared. That means 4 squared + 5 squared = 41. That means RT equals Square root of 41. Then you do RT squared plus QR squared = QT squared. 41 + 4 = 45 squared. QT = square root 45. Then you use PQ now and with QT you can find PT.

3 squared = 9. 9 plus PT squared = QT squared. Pt squared equals 36 and PT equals 6. PT equals 6, so how can I answer this question??
Sorry I meant RT2+ RS2 = TS2

#### ironsheep

##### Junior Member
Sorry I meant RT2+ RS2 = TS2

Wait, you said you can only use A square + B squared = C squared for right triangles only

#### Jomo

##### Elite Member
Use my hint above (Here is a better hint. You have a triangle that has two sides of length r and s (assume r<.s) The length of the 3rd side is between s-r and s+r ) to first find the range for the length of PR. Please post back with that result.

#### ironsheep

##### Junior Member
Why are you talking about RS being less than ST?

#### Jomo

##### Elite Member
Why are you talking about RS being less than ST?
Why are you talking about RS being less than ST?
Never said that

Step 1--- Draw line PR
Step 2---Look at triangle PRQ and decide what the length of PR can be.

#### ironsheep

##### Junior Member
I drew triangle PQR and I guess PR could be 4. QR is 2 and PQ is 3, so PR is maybe 4 or it could be 5

#### Jomo

##### Elite Member
I drew triangle PQR and I guess PR could be 4. QR is 2 and PQ is 3, so PR is maybe 4 or it could be 5
NO, no guessing. You know two sides of the triangle. If one side is length r and the other side is length s (say s>r), then the length of the third side is between s-r and s+r.
So the length of that 3rd unknown side is between ...?

#### ironsheep

##### Junior Member
Why would the length be between the (Qr-QP= 1) and (QR + QP = 5), why are you doing between ranges of 1 and 5? What kind of geometry concept is this?

#### Jomo

##### Elite Member
.The largest an angle can b in a triangle is when the angle is close to 180, that is almost a straight line. If one side is r and the other side has length s, then that 3rd side will almost be r+s. Draw it and see it for yourself.
The smallest an angle can be in a triangle is when the angle is close to 0. So the two sides of the triangle are almost on top of another. The 3rd side will be close to the difference of the two sides. Draw it and see for yourself.
So the length of the 3rd side of a triangle is ALWAYS between the difference of the other two sides and the sum of the other two sides.

Is this all clear?