Question

Two sides of a rectangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is it's third side?

Answer 1

Appropriate Question:

• Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is it's third side?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━

Given that,

• AB = 12 cm

• BC = 14 cm

• Perimeter = 36 cm

Need To find:

• Third side, AC = ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━

As we know that,

$\bigstar\;\boxed{\frak{Perimeter_{\;triangle} = a + b + c}}$

where,

• a, b & c are the three sides of triangle.

⠀⠀

⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{Putting\;the\:given\;values\: :}}$⠀

⠀⠀⠀⠀⠀

$\dashrightarrow\sf Perimeter_{ \: (triangle)} = a + b + c \\\\\\\dashrightarrow\sf AB + BC + AC = 36\\\\\\\dashrightarrow\sf 12 + 14 + AC=36\\\\\\\dashrightarrow\sf 26 + AC=36\\\\\\\dashrightarrow\sf AC = 36 - 26\\\\\\\dashrightarrow\underline{ \boxed{\frak{\pmb{\purple{AC = 10}}}}}\;\bigstar$

⠀⠀

$\therefore{\underline{\textsf{Hence, the third side of triangle is \textbf{10 cm}.}}}$

⠀⠀⠀⠀⠀⠀⠀⠀

Answer 2

Answer:

Given :-

First side = 12 cm

Second side = 14 cm

Perimeter = 36 cm

To Find :-

Third side

Solution :-

Let us assume that

✯ Third side = x ✯

Now

Perimeter = Sum of all side

36 = 12 + 14 + x

36 = 26 + x

36 - 26 = x

10 = x

Hence,

The third side of the triangle is 10 cm