Question

The sides of a triangle are three consecutive multiples of 9. If the perimeter of the
triangle is 54 m, find the length of the sides of triangle​

Answer 1

ATQ,

the sides of a triangle are three consecutive multiples of 9.

let the first side be x. therefore second and third side are x + 9 and x + 18 respectively.

given perimeter of the triangle = 54m

we know that,

perimeter of a triangle = sum of all three sides

➡ x + x + 9 + x + 18 = 54m

➡ 3x + 27 = 54m

➡ 3x = 54 - 27

➡ 3x = 27

➡ x = 27/3

➡ x = 9m

hence, the all three sides of the triangle are :-

• x = 9m

• x + 9 = 9 + 9 = 18m

• x + 18 = 9 + 18 = 27m

VERIFICATION :-

perimeter of the triangle = 9 + 18 + 27

= 27 + 27

= 54m

hence verified!

Answer 2

$\huge{\underline{\underline{\mathfrak{Answer:-}}}}$

$\large{\sf{9}}$

$\huge{\underline{\underline{\mathfrak{Explanation:-}}}}$

$\large{\sf{let \: The \: Sides \: Be \: x, x+9 , x+18 }}$

$\large{\sf{Perimeter \: = \: 54m}}$

$\large{\sf{So,}}$

$\large{\sf{x \: x+9 \: x+18 \: = \: 54}}$

$\large{\rightarrow{\sf{3x \: + \: 27 \: = \: 54}}}$

$\large{\sf{3x \: = \: 54-27}}$

$\large{\sf{3x \: = \: 27}}$

$\large{\sf{x \:=\: {\frac{27}{3}}}}$

$\large{\sf{x \: = \: 9}}$

$\huge{\bf{Sides \: are :-}}$

$\large{\star{\boxed{\sf{x \: = \: 9 m}}}}$

$\large{\sf{9 \: + \: 9}}$

$\large{\star{\boxed{\sf{x \: = \: 18 m}}}}$

$\large{\sf{9 \: + \: 18}}$

$\large{\star{\boxed{\sf{x \: = \: 27 m}}}}$