Question

please solve this sum​

Answer 1

Given :   Three Coordinates of triangels & area of triangle

To find :  Perimeter of Triangle

Solution:

Coordinates of vertex are

(0 , 15) , ( - 5 , 3)  & ( a  , 3)

Area of  triangle  =  (1/2) |  0 (3 - 3) - 5(3 - 15) + a(15 - 3) |

= (1/2) | 0 + 60 + 12a |  

= |  30 + 6a |   = 126

=> 30 + 6a  = 126    or 30 + 6a =  - 126

=> 6a = 96          or 6a = -156

=> a = 16            or  a  = - 26

From figure its very clear that

a  = 16

AB = √(16 -(-5))² + (3 - 3)²  = 16

AC  = √(0 -(-5))² + (15 - 3)²  = 13

BC = √(0 - 16 )² + (15 - 3)²  = 20

Perimeter of ABC = 16  + 13  +  20   =  49  units

Another method to find a

Draw CD ⊥ AB  

AB is parallel to x axis   Hence CD ⊥ y axis ( actually y axis in this case)

=> D = (0 , 3)

CD = 15 - 3  = 12

(1/2) * AB * CD = 126

=> AB  = 21

=> a -(-5) = 21  => a   = 16

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