A triangle and a parallelogram have the same base and the same area at the side of the triangle are 126cm 120cm and 130cm and parallelogram stand on the base 120 cm find the corresponding reight of the parallelogram

Answers (1)

Side of triangle 126cm, 120cm, and 130cm 

its semi-perimeter,     

                               $$s = fraca+b+c2$$

Now, 

                        $$s = frac126+120+1302= frac3762 = 188 cm $$

We use Heron's formula,  Area of triangle 

                                      $$ = sqrt s(s-a)(s-b)(s-c) $$

   Put the value, Area of triangle 

                                               $$ = sqrt 188(188-126)(188-120)(188-130) $$ \$$ $$= sqrt 188 imes 62 imes 68 imes 58 $$\$$ $$= 6780.21cm^2 $$

      Since a parallelogram and a triangle have the same base and same area, now

Area of parallelogram = Area of trianble 

                                                              $$ 120 imes height(h) = 6780.21 $$\$$ $$ h = 56.50 cm $$

Hence, corresponding height of parallelogram with base 120cm = 56.50 cm 

 

 

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