Question

If SQ=94, QR=97, SR=115, TU=63, and VU=74.8, find the perimeter of △TUV. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Answer 1

Answer:

198.85

Step-by-step explanation:

Similar triangles:

In ΔTUV & ΔQRS,

∠T = ∠Q

∠U = ∠R

∠V = ∠S

ΔTUV ~ ΔQRS by AAA similarity criteria.

If two triangles are similar, then their corresponding sides are in same proportion.

       $\sf \dfrac{TU}{QR}=\dfrac{VU}{SR}=\dfrac{TV}{SQ}$

  TU =63; VU = 74.8

  QR = 97; SR = 115 ; SQ = 94    

To find the value of TV,

       $\sf \dfrac{TU}{QR}=\dfrac{TV}{SQ}$

        $\sf \dfrac{63}{97}=\dfrac{TV}{94}\\\\\\\dfrac{63}{97}*94=TV$

           TV = 61.05

As we know all the three sides of triangle TUV, we can find the perimeter.

Perimeter of triangle TUV = TU + UV + TV

                                           = 63 + 74.8 + 61.05

                                           = 198.85