What is the perimeter of a triangle with corners at $(6, 5)$ $(6 ,5 )$ , $(8, 2)$ $(8 ,2 )$ , and $(4, 7)$ $(4 ,7 )$ ?

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What is the perimeter of a triangle with corners at $(6, 5)$ $(6 ,5 )$ , $(8, 2)$ $(8 ,2 )$ , and $(4, 7)$ $(4 ,7 )$ ?

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Answer 1 · 2018-03-03T10:38:11

Perimeter = 62

Explanation:

Let $(6, 5)$ $(6,5)$ = $A$ $A$ , $(8, 2)$ $(8,2)$ = $B$ $B$ and $(4, 7)$ $(4,7)$ = $C$ $C$
Formula of distance between points is :
$\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $sqrt ((x_2-x_1)^2+(y_2-y_1)^2$
Find the distance between A and B:
Let $(6, 5)$ $(6,5)$ = $(x_{1}, y_{1})$ $(x_1,y_1)$ $and$ $and$ $(8, 2)$ $(8,2)$ = $(x_{2}, y_{2})$ $(x_2,y_2)$
$\Rightarrow$ $=>$ $\sqrt{{(8 - 6)}^{2} + {(2 - 5)}^{2}}$ $sqrt ((8-6)^2+(2-5)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(2)}^{2} + {(- 3)}^{2}}$ $sqrt ((2)^2+(-3)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(4 + 9)}^{2}}$ $sqrt ((4+9)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(13)}^{2}}$ $sqrt ((13)^2)$
$\Rightarrow$ $=>$ $13$ $13$

Find the distance between B and C:
Let $(8, 2)$ $(8,2)$ = $(x_{1}, y_{1})$ $(x_1,y_1)$ $and$ $and$ $(4, 7)$ $(4,7)$ = $(x_{2}, y_{2})$ $(x_2,y_2)$
$\Rightarrow$ $=>$ $\sqrt{{(4 - 8)}^{2} + {(7 - 2)}^{2}}$ $sqrt ((4-8)^2+(7-2)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(- 4)}^{2} + {(5)}^{2}}$ $sqrt ((-4)^2+(5)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(16 + 25)}^{2}}$ $sqrt ((16+25)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(41)}^{2}}$ $sqrt ((41)^2)$
$\Rightarrow$ $=>$ $41$ $41$

Find the distance between C and A:
Let $(4, 7)$ $(4,7)$ = $(x_{1}, y_{1})$ $(x_1,y_1)$ $and$ $and$ $(6, 5)$ $(6,5)$ = $(x_{2}, y_{2})$ $(x_2,y_2)$
$\Rightarrow$ $=>$ $\sqrt{{(6 - 4)}^{2} + {(5 - 7)}^{2}}$ $sqrt ((6-4)^2+(5-7)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(2)}^{2} + {(- 2)}^{2}}$ $sqrt ((2)^2+(-2)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(4 + 4)}^{2}}$ $sqrt ((4+4)^2)$
$\Rightarrow$ $=>$ $\sqrt{{(8)}^{2}}$ $sqrt ((8)^2)$
$\Rightarrow$ $=>$ $8$ $8$

Perimeter = $A B + B C + C A$ $AB + BC + CA$
$\Rightarrow$ $=>$ $13 + 41 + 8$ $13 + 41 + 8$
$\Rightarrow$ $=>$ $62$ $62$

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What is the perimeter of a triangle with corners at $(6, 5)$ $(6 ,5 )$ , $(8, 2)$ $(8 ,2 )$ , and $(4, 7)$ $(4 ,7 )$ ?

1 Answer

Explanation:

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