Question

The Perimeter of a triangle is 18x + 12 y + 13 z and two of its sides
are 5x + 3y -4z and 6x + 5y + 7z. Find the third side.

Answer 1

⠀⠀▪︎⠀Perimeter of triangle = 18x + 12y + 13z

⠀⠀▪︎⠀Two sides of triangles = 5x + 3y - 4z & 6x + 5y + 7z

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

As we know that,

⠀⠀⠀

$\star\:{\underline{\boxed{\frak{Perimeter_{\;(triangle)} = a + b + c}}}}$

⠀⠀⠀

Where,

• a, b and c are sides of triangle.

⠀⠀⠀

❍ Let's consider c be the third side of triangle and a and b be the two given sides.

⠀⠀⠀

Now, Putting values in Formula,

⠀⠀⠀

$\dashrightarrow\sf 18x + 12x + 13z = (5x + 3y - 4z) + (6x + 5y + 7z) + c\\\\\\ \dashrightarrow\sf 18x + 12x + 13z = (11x + 8y + 3z) + c\\\\\\ \dashrightarrow\sf c = (18x + 12x + 13z) - (11x + 8y + 3z)\\\\\\ \dashrightarrow{\underline{\boxed{\sf{\purple{c = 7x + 4y + 10z}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\:third\:side\:of\:triangle\:is\: {\pmb{7x + 4y + 10z}}.}}}$

Answer 2

Answer:

Given :

• The perimeter of a triangle is 18x + 12y + 13z and of its sides are 5x + 3y - 4z and 6x + 5y + 7z.

To Find :-

• What is the third side.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Perimeter\: of\: triangle =\: Sum\: of\: all\: sides}}}$

Solution :-

Let, the third side of a triangle be c

Given :

• Perimeter = 18x + 12y + 13z
• First side = 5x + 3y - 4z
• Second side = 6x + 5y + 7z

According to the question by using the formula we get,

$\implies \sf (18x + 12y + 13z) =\: (5x + 3y - 4z) +\: (6x + 5y + 7z) + c$

$\implies \sf (18x + 12y + 13z) =\: 5x + 6x + 3y + 5y + (- 4z + 7z) + c$

$\implies \sf (18x + 12y + 13z) =\: (11x + 8y + 3z) + c$

$\implies \sf (18x + 12y + 13z) - (11x + 8y + 3z) =\: c$

$\implies \sf 18x - 11x + 12y - 8y + 13z - 3z =\: c$

$\implies \sf 7x + 4y + 10z =\: c$

$\implies \sf\bold{\red{c =\: 7x + 4y + 10z}}$

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