Question

please solve this sums​

Answer 1

Answer:

Q1) 1. QC= 12.5 cm(units)

3. they are parallel since the ratio of the sides are equal

Step-by-step explanation:

1. Let QC be 'x' .

AP = 3 cm

BP = 7.5 cm

AQ = 5 cm

PQ║BC

∴ AP/BP = AQ/QC. ( BPT)

⇒3/7.5 = 5/x

Cross Multipy to get :

3x = 5 × 7.5

⇒3x = 37.5

⇒ x = 37.5/3

       = 12.5

∴ QC = 12.5 cm

3. GIVEN :  PR = 18 units

                  AR = 8 units

                  PQ = 27 units

                  PB = 15 units

TO PROVE : AB ║ RQ

PROOF : PB +BQ = PQ

            ⇒15 + BQ  = 27

            ∴ BQ = 27 - 15

                      =  12

               AR/PR = BQ/PQ

          ⇒ 8/18  = 12 / 27

               By cross multiplication ,we get

               8 × 27 = 18 × 12

           ⇒  216    =  216

             ∴ LHS  = RHS

             ⇒ The ratio of the sides of the triangle is equal

             ∴ AB ║ RQ  ( Converse of BPT )

               Hence Proved .