Can someone answer these for me please?

Question

∆ABC~∆XYZ with m∠A=m∠X and m∠B=m∠Y and m∠C=m∠Z. AB, BC, and AC are 5 inches, 12 inches, and 13 inches respectively. XY is 9 inches, find XZ (to the nearest tenth).

 

The perimeter of ∆PQR is 65, PQ=15, ∆PQR~∆STU, and ST=12. What is the perimeter of ∆STU?

Answer 1

 

Because they are similar triangles, their sides are in proportion.

 

AB      AC

--- = -----

XY      XZ

 

5        13

--- = ---

9        ?

 

Cross multiplies:

 

5 * ? = 9 * 13

 

? = 9 * 13 / 5 = 23.4

 

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The ratio of PQ:ST = PQ/ST = 15/12 = 5/4
That is ST * 5/4 = PQ
So that means ST = 4/5*PQ
15 + QR + PR = 65

QR + PR = 50

TU = 4/5*QR ---> QR = 5/4*TU

SU = 4/5*PR ---> PR = 5/4*SU


5/4*TU + 5/4*Su = 50

5/4 ( TU + SU ) = 50

TU + SU = 50/5*4 = 40

THe perimeter is ST + TU + SU =

ST + (TU + SU) =
12 + 40 = 52

Note that 52 * 5/4 = 13*5 = 65