Question

Are the triangles similar? If so, what is the scale factor of ΔRPQ to ΔVAQ?

A)NO


B)YES; 2:1
C)YES; 2:3
D) YES; 3:4

Answer 1

Yes 2:1 you know this because the short sides, 3 and 6 are in the same ratio as the long sides, 4 and 8

Answer 2

Option B) YES; 2:1

Explanation:

In these triangles ΔRPQ and ΔVAQ we have been given few measurements like

∠RPQ = ∠VAQ = 90°

Length of AV =3, AQ = 4 &

Length of RP =6, PQ = 8

Now we have been asked about the scale factor of these two triangle and similarity between them.

As we know if two sides of a triangle is in the same ratio of the other triangle and angle between these sides is same then triangles are similar.

In other words ratio of sides RP:AV = PQ:AQ

⇒
`(RP)/(AV) = (PQ)/(AQ)`

⇒
`(6)/(3) = (8)/(4)`

⇒ 2:1 =2:1

And angle between them ∠RPQ = ∠VAQ = 90°

Therefore bothe the triangles are following rule of SAS so similar with a scale factor of 2:1.