Triangle ABC is similar to triangle PQR . AB corresponds to PQ and BC corresponds to QR. lf AB = 9, BC = 12, CA = 6, and PQ = 3, what are the lengths of QR and RP?

Answer 1

#QR=4# and #RP=2#

As #DeltaABC~~DeltaPQR# and #AB# corresponds to #PQ# and #BC# corresponds to #QR#, we have,

Then we have

#(AB)/(PQ)=(BC)/(QR)=(CA)/(RP)#

Hence #9/3=12/(QR)=6/(RP)#

i.e. #9/3=12/(QR)#

or #QR=(3xx12)/9=36/9=4#

and #9/3=6/(RP)#

or #RP=(3xx6)/9=18/9=2#

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Answer 2

To find the lengths of QR and RP in triangle PQR, we'll use the properties of similar triangles.

First, we'll find the scale factor between the two triangles. The scale factor is the ratio of corresponding sides. In this case, the ratio of AB to PQ:

[ \text{Scale Factor} = \frac{AB}{PQ} = \frac{9}{3} = 3 ]

Now, we'll use this scale factor to find the lengths of QR and RP.

[ QR = BC \times \text{Scale Factor} = 12 \times 3 = 36 ]

[ RP = CA \times \text{Scale Factor} = 6 \times 3 = 18 ]

So, the length of QR is 36 units, and the length of RP is 18 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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